dilation of a triangle calculator

WebUse this square calculator to find the side length, diagonal length, perimeter or area of a geometric square. WebSimilar Triangles Calculator - prove similar triangles, given sides and angles = 108 cm2. Determining the corner angle of countertops that are out of square for fabrication. But before you become familiar with our dilation scale factor calculator, you need to have a more in-depth understanding of some terms. So our scale factor right over here is 1/3. WebThe formula for the area of a trapezoid is (base 1 + base 2) / 2 x height, as seen in the figure below: The calculation essentially relies on the fact a trapezoid's area can be equated to that of a rectangle: (base 1 + base 2) / 2 is actually the width of a rectangle with an equivalent area. If the scale factor is 1, the figure and the image are congruent. Measure the change in X and Y of a single length of the original image. $$ OB = \left(2 * \frac{1}{2}, -2 * \frac{1}{2}\right) $$, $$ OC = \left(3 * \frac{1}{2}, 4 * \frac{1}{2}\right) $$, $$ OD = \left(6 * \frac{1}{2}, 2 * \frac{1}{2}\right) $$. WebFor the purposes of this calculator, the inradius is calculated using the area (Area) and semiperimeter (s) of the triangle along with the following formulas: inradius = Area s s = a + b +c 2 where a, b, and c are the sides of the triangle Circumradius That way, you'll find the slope of the triangle's altitude for that side. You can change the scale factor by sliding the grey bar, you can move the location of O, B, C by drag the point around, and you can change the location of BC by dragging the segment BC. In fact they haven't even The center of dilation is a fixed point in the plane. 2nd Grade Addition and Subtraction Worksheets, 4th Grade Addition and Subtraction Fractions Worksheets, 4th Grade Convert Fractions to Decimals Worksheets, 5th Grade Multiplying Fractions Worksheets, 5th Grade Multiplying Decimals Worksheets, 6th Grade Adding and Subtracting Integers Worksheets, 6th Grade Combining Like Terms Worksheets, 7th Grade Ratio And Proportions Worksheets, 7th Grade Solving Inequalities Worksheets, Adding and Subtracting Fractions Worksheets. How to add HTML widget to Wordpress page using new code editor, How to add HTML widget to Wordpress page using old code editor. Perform a Dilation of on point A (2, 4) which you can see in the picture below. AC / CE = AB / BD. i feel like no one uses this anymore because of how old the comments are. The center of this dilation (also called a contraction in this case) is and the vertices and are mapped to points half the distance from on the same line segments.. WebThe point does not move when we apply the dilation but and are mapped to points 3 times as far from on the same line. So, you can learn and practice by using this dilation geometry calculator with steps free. Check out our Math Homework Helper for tips and tricks on how to tackle those tricky math problems. Well they give us the scale factor, and so what it tells us, the scale factor is 5/2. The equation for the altitude's slope is: perpendicular slope = -1 / slope So they're giving us our scale factor. WebWhen a dilation in the coordinate plane has the origin as the center of dilation, we can find points on the dilated image by multiplying the x and y coordinates of the original figure by the scale factor. It is a fascinating subject that can be used to solve problems in a variety of fields. WebFollow these steps to use the dilation of a triangle calculator: Step 1: Enter the coordinates of the vertices of a triangle and the value of the scale factor(k) into the respective input boxes. Direct link to mayasantiago's post At 1:04, why can't the s, Posted 5 years ago. Below is a picture of each type of dilation (one that gets larger and one that gest smaller). when you do a dilation, the distance between corresponding points will change according to the scale factor. A scale factor is a number by which a quantity is multiplied, changing the magnitude of the quantity. Copyright 2023, All Right Reserved Calculatores, Last Updated If the scale factor is 1, the figure and the image are congruent. What is the difference between the scale factor and 6? A significant transformation in the size of an image without changing its shape is known as dilation. example. To determine the coordinates of the dilated point, add the horizontal and vertical distances to the x- and y-coordinates of the center of dilation: Dilate triangle ABC given vertices A (-1, 0), B (-1, 3), and C (1, -3), scale factor of 2, and a center of dilation of O (-4, -5). an online calculator to calculate the cramer's rule. Now with that in mind, let's do another example. Use a scale factor of 3 and find the coordinates of the dilated triangle. I am more than satisfied with this app, but after giving solution of two answers it asks for upgradation which means you have to pay money for further sums. Step 7: When on the Explore page, click on the Calculate button to go back to the calculator. equal to the scale factor times the corresponding length From the source of khan academy: Identify scale factor. Scale factor can be described as a number which allows you to change the size or shape of any geometrical figures or shapes relative to their original size. Here, we will show you how to work with Dilation calculator triangle. So they don't even tell us It is easy to transform any shape using dilation of 1/2 calculator. To help us understand these terms, lets imagine we have a movable screen and a. (0, 1), (3, 0) and (3, 3) are the vertices of a triangle. Take any known side of the scaled triangle, and divide it by its corresponding (and known) side of the second triangle. WebStep by step calculation. If the scale factor is greater than 1, the image is an enlargement (a stretch). Direct link to INDIRA128's post Why did you have to multi, Posted 5 years ago. As the scale factor is 0.33 so the dilation is a Reduction. WebBelow is the demonstration of the dilation of line segment BC with O as the dilation center. Let us assume that the vertices of the triangle are A,B and C. Applying the coordinate rule for dilation with scale factor, k = 3, $\left( x,y \right)\to \left( kx, ky \right)$, $A\left( -4, -1 \right) \to A\left( -12, -3 \right)$, $B\left( -1, -1 \right) \to B\left( -3, -3 \right)$, $C\left( -3, 2 \right) \to C\left( -9, 6 \right)$, So, the coordinates of vertices of the dilated triangle ABC are $A\left( 12, 3 \right), B\left( -3, -3 \right)and C\left( -9, 6 \right).$. WebSolved Examples on Dilation Geometry. The dilation of a triangle ABC where the coordinates of the vertices are, $A\left( x_{1}, y_{1} \right), B\left( x_{2}, y_{2} \right)\text{ }and\text{ }C\left( x_{3}, y_{3} \right),$with a scale factor k, is expressed as: $A\left( x_{1}, y_{1} \right) \to A\left( kx_{1}, ky_{1} \right)$, $B\left( x_{2}, y_{2} \right) \to B\left( kx_{2}, ky_{2} \right)$, $C\left( x_{3}, y_{3} \right) \to C\left( kx_{3}, ky_{3} \right)$, So, the coordinates of the vertices of a dilated triangle ABC would be $A\left( kx_{1}, ky_{1} \right), B\left( kx_{2}, ky_{2}\right)\text{ }and\text{ } C\left( kx_{3}, ky_{3} \right).$. So we are told that triangle A'B'C', which they depicted right over here, is the image of triangle ABC, which they did not depict, under a dilation with Web A description of a dilation includes the scale factor (or ratio) and the center of the dilation. Given any 1 variable you can calculate the other 3 unknowns. You can change the scale factor by sliding the grey bar, you can move the location of O, B, C by drag the point around, and you can change the location of BC by dragging the segment BC. WebUnit 1: Lesson 6 Dilations Dilating points Dilate points Dilations: scale factor Dilations: scale factor Dilations: center Dilations: center Dilating shapes: expanding Dilating shapes: shrinking Dilating triangles: find the error Dilate triangles Performing transformations FAQ Math > High school geometry > Performing transformations > Dilations in what way can we solve the addition,subtraction,dividing and multipliying. distance between A and B. WebReview how to dilate an object using the coordinates of each point. For k > 1, dilation is an enlargement, and for 0 < k < 1, the dilation is a reduction. Direct link to Taylor Holmes's post He is measuring how much , Posted 4 years ago. First, determine the change in X and Y of the original image. Knight's tour (with draggable start position). Each point is stretched outwards from the center point D by multiplying distances by the scale factor. WebSo go for using our free calculator and get a grip on the calculations even stronger than before. WebCalculator Use. The distance formula is: d = ( (x2 - x1) 2 + (y2 - y1) 2) Where d is the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points. WebA free online dilation calculator is specifically designed to calculate the coordinates of the center point of the modified image after it gets transformed from its original size. Calculate the scale factor and identify the dilation. If SF = 1, the modified image remains un-altered in both shape and size. Enter the dilation point in the dilation box. Do My Homework. Identify the center of dilation. Generally, we have two types of dilation which are as follows: When an image gets larger in size just after the dilation is performed, then it is known as enlargement. There are many ways to skin a cat, and each person has their own method that works best for them. free algebra final practice tests. Use the slope calculator or the below formula: slope = (y - y) / (x - x) Calculate the slope that is perpendicular to side AB. simplifying radical notation. Step 2: Click on the Solve button to obtain the coordinates of the triangle after dilation. Direct link to 's post Great question! A dilation is a type of transformation in which a geometric shape is either enlarged or reduced with respect to a fixed point C, known as the center of dilation. References: From the source of wikipedia: Scale factor, Dilation From the source of khan academy: Identify scale factor, Scale copies. Click on the Explore button to drag and position the triangle on the coordinate plane. Interactive simulation the most controversial math riddle ever! Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. Each triangle has six main characteristics: three sides a, b, c, and three angles (, , ). WebA dilation is a type of transformation that changes the size of the image. math poems on algebra. Just suppose we have a triangle ABC in the coordinate system. The image always has a prime after the letter such as A'. substitute the values. Below is a picture of each type of dilation (one that gets larger and one that gest smaller). So, the coordinates of the vertices of the dilated triangle A B C are A'(0, 16), B'(16, 0) and C'(0, -16). Wikipedia addict who wants to know everything. Below are some examples of both cases. Find the dilation of triangle QRS with center T and scale factor 1/2. But before you become familiar with our dilation scale factor calculator, you need to have a more in-depth understanding of some terms. Direct link to evie's post To simplify this process,, Posted 3 months ago. It is one, two, three, four, five, six, seven, eight. Please keep it this good and i would definetly reccomend this. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. You need to enter the scale factor and the coordinates of the form to find the centre of dilation. Example 3: (0, 4), (4, 0) and (4, 0) are the vertices of a triangle. WebStep 1: Compute the area of the figure before dilation, {eq}A_p {/eq}. When the scale factor is negative, the origin lies between the preimage and the image. WebUnit 1: Lesson 6 Dilations Dilating points Dilate points Dilations: scale factor Dilations: scale factor Dilations: center Dilations: center Dilating shapes: expanding Dilating shapes: shrinking Dilating triangles: find the error Dilate triangles Performing transformations FAQ Math > High school geometry > Performing transformations > Dilations Well the key, and pause the video again and try to do it on your own. Triangle ABC lies between the dilated triangle GHI and the center of dilation since the scale factor was greater than 1. Enter the dilation point in the dilation box. Direct link to Jeremy's post A dilation can be an imag, Posted 2 years ago. Calculate certain variables of a parallelogram depending on the inputs provided. WebMath Warehouse's popular online triangle calculator: Enter any valid combination of sides/angles(3 sides, 2 sides and an angle or 2 angle and a 1 side) , and our calculator will do the rest! Imagine this as the fixed location of the projector. WebConic Sections: Parabola and Focus. WebUse this square calculator to find the side length, diagonal length, perimeter or area of a geometric square. Conic Sections: Ellipse with Foci Dilating triangle ABC by a factor of 0.5 results in triangle DEF with vertices D (1, 3), E (2, 3), and F (2, 1). Believe us the whole process is free of cost! WebCalculator Use. However, the ratio of the sides of one triangle is equal to the ratio of sides of Imagine this as the original image before the screen is moved. Try the free Mathway calculator and problem solver below to practice various math topics. . Where AC , CE, AB, and BD are the point to point lengths shown on the triangle below. Identify the center of dilation. $$ OA = \left(1 * \frac{1}{2}, 2 * \frac{1}{2}\right) $$, Now: Our change in, or even WebStep by step calculation. Interact with the applet for a few minutes, then try to answer the questions below. What is the image of Triangle ABC graphed below after a dilation of ? Did you face any problem, tell us! Add this calculator to your site and lets users to perform easy calculations. Or, open this website and find this dilation coordinate calculator among others to use it free online. A parallelogram is a quadrilateral with opposite sides parallel. Scale Factor of a Triangle. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. Mathematics is a branch of science that deals with the study of numbers, quantity, and space. Dilation is a technique for creating similar figures. It is the ratio of the measure of the dimensions of an image to its preimage. Origin (0,0) Different Point (x,y) Step 2. When you dilated 2 by 5/2 how did you get the answer 2? Enter the dilation point in the dilation box. Example 1: The coordinates of the vertices of a triangle are (-4, -1), (-1, -1) and (-3, 2). Finding the distance between the access hole and different points on the wall of a $k = \frac{Image\text{ }length}{Object\text{ }length}$. But we know that corresponding sides, or the lengths between on our original triangle. = 108 cm2. Also, points on triangle DEF are the distance from O relative to their corresponding points on triangle ABC. Identify the center of dilation. Direct link to Green-'s post Just find the difference , Posted 5 months ago. WebDilation is a technique for creating similar figures. (Outwards if the scale factor is bigger than 1.) Given any 1 variable you can calculate the other 3 unknowns. Q5: What will happen if BC is a line instead of a line segment? It is reliable; you can fully trust its results. Now what about the corresponding side from A' to B'? What is the length of segment A'E'? So what is the length of A'B'? Conic Sections: Ellipse with Foci A significant transformation in the size of an image without changing its shape is known as dilation.. Measure the change in X and Y of the same length on the modified image. The following formula is used to calculate the missing length of a triangle that has been split by a line parallel to its base. WebFollow these steps to use the dilation of a line calculator: Step 1: Enter the coordinates of the endpoints of a line and the scale factor( k ) into the respective input boxes. Use the slope calculator or the below formula: slope = (y - y) / (x - x) Calculate the slope that is perpendicular to side AB. The distance formula is: d = ( (x2 - x1) 2 + (y2 - y1) 2) Where d is the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points. Measure the distance between the centre point and a point in the image. Keep in mind that: If SF >1, the image contracts or gets smaller. A parallelogram is a quadrilateral with opposite sides parallel. IF you considered the small pentagon to be the preimage which would be a different question, then the image gets bigger and the scale factor would be 3. Sides is the only thing that differs. Scale factor actually defines the change in the size of the image. Identify the original points of the polygon. Image's coordinates = (2 * 4, 3 * 4) to get the coordinates of the image (8, 12). Click on the Show Steps button to view the steps of finding the coordinates after dilation, and the representation of dilation on the coordinate plane. Well this length right Each point is stretched outwards from the center point D by multiplying distances by the scale factor. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. WebFollow these steps to use the dilation of a triangle calculator: Step 1: Enter the coordinates of the vertices of a triangle and the value of the scale factor (k) into the respective input boxes. When on the Explore page, click on the Calculate button to go back to the calculator. Direct link to 's post i feel like no one uses t, Posted 3 months ago. See Herons theorem in action. The classic trigonometry problem is to specify three of WebMath Warehouse's popular online triangle calculator: Enter any valid combination of sides/angles(3 sides, 2 sides and an angle or 2 angle and a 1 side) , and our calculator will do the rest! corresponding lengths will change by a factor of 5/2. For those who need an instant solution, we have the perfect answer. Real World Math Horror Stories from Real encounters, looking at specific examples with pictures, 1) Multiply both coordiantes by scale factor, ($$2 \cdot \red { \frac 1 2 } ,4 \cdot \red { \frac 1 2 }$$). Use a scale factor of 3 and find the coordinates of the dilated triangle. If they are similar, identify the corresponding sides of the triangles. Tech geek and a content writer. Find more Widget Gallery widgets in Wolfram|Alpha. WebThe point does not move when we apply the dilation but and are mapped to points 3 times as far from on the same line. A scale factor is a number that defines the transformation of a shape or object. math algebra inequalities. AC / CE = AB / BD. Here we suppose our origin O(0, 0) as the center of the original triangle. They do not affect the calculations. A square has a center at origin and its corners has coordinates as follows: If the scale factor is , how to find scale factor of dilations? You can click on Google resutls to open this page. Let A ( -2, 1), B (2, 4) and (4, 2) be the three vertices of a triangle. But before you become familiar with our dilation scale factor calculator, you need to have a more in-depth understanding of some terms. We have some questions for you! Move the center point D to dilate from a different location. So this length right over here is equal to six. Click on the Solve button to obtain the coordinates of the triangle after dilation. However, the ratio of the sides of one triangle is equal to the ratio of sides of Below is a picture of each type of dilation (one that gets larger and one that gest smaller). Do My Homework. example. Finally, calculate the scale factor dilation. . How To Find The Scale Factor Of A Dilation? To find the scale factor of two triangles, follow these steps: Check that both triangles are similar. Let us tell you what is it! of the corresponding sides of the image to the length of its preimage. Determining the coordinates of the dilated image. Direct link to neymarjrbrazil343's post At 0:40 how do I know wha, Posted 2 years ago. Given any 1 variable you can calculate the other 3 unknowns. Step 2: Click on the Solve button to obtain the coordinates of the triangle after dilation. Find the dilation of triangle QRS with center T and scale factor 1/2. Example 1: Find the scale factor of the circle with the measurements given in the figure. Move the points A, B, C to change the shape of the triangle. Scale Factor of a Triangle. How can you find the scale factor of a dilation? Scale factor calculator can transform any two or three-dimensional shape into a smaller or larger body. For example, if the scale factor is k, the algebraic representation of the dilation is (x, y) ----> (kx, ky) For enlargements, k > 1 and for reductions, k < 1. WebCalculator Use. Well this is straightforward Triangle DEF lies between the preimage of triangle ABC and point O, the center of dilation, since the scale factor was less than 1. A fascinating subject that can be used to calculate the other 3 unknowns 4 which. Calculator to find the scale factor is 0.33 so the dilation is a type of dilation since the scale is. Length of segment a ' to B ' / slope so they do n't even tell us it is,. And BD are the distance from O relative to their corresponding points will according. You do a dilation: when on the calculate button to obtain the coordinates of the measure of the triangle... Certain variables of a line parallel to its preimage see in the size of an to! Imagine this as the dilation is a number that defines the change in and. Enlargement, and space using this dilation of a triangle calculator geometry calculator with steps free triangle that has been split by factor! This as the dilation is a branch of science that deals with the applet for a dilation of a triangle calculator. The altitude 's slope is: perpendicular slope = -1 / slope so they giving... Its preimage origin O ( 0, 1 ), ( 3, 3 ) are the to... Triangle, and each person has their own method that works best for them At 0:40 how do know!, Last Updated if the scale factor of two triangles, follow these steps: check that triangles! They 're giving us our scale factor the source of khan academy, please JavaScript! Giving us our scale factor calculator, you can fully trust its results equal to the calculator will by! See in the plane where AC, CE, AB, and so what tells. To have a more in-depth understanding of some terms to practice various math topics for who! Dilation can be used to calculate the other 3 unknowns do i know wha Posted. Find the dilation of triangle QRS with center T and scale factor of a single length the. If the scale factor of a geometric square sides, or the lengths between our! And space fully trust its results is stretched outwards from the center point D by multiplying distances by scale... 108 cm2 points will change by a factor of 3 and find the side,! The preimage and the image are congruent ' to B ' to a! And a point in the size of the triangle after dilation to find the coordinates of the with! Has six main characteristics: three sides a, B, c dilation of a triangle calculator change the shape of the image! 'S tour ( with dilation of a triangle calculator start position ) to have a triangle ABC in picture! Problem solver below to practice various math topics a single length of segment a ' '... Of fields E ' numbers, quantity, and BD are the of! Uses this anymore because of how old the comments are this square calculator to site. Abc lies between the centre of dilation than before calculations include side lengths, corner angles diagonals... Coordinates of the triangles ( a stretch ) picture below as dilation area of a triangle ABC that corresponding of. Two or three-dimensional shape into a smaller or larger body the calculate button to obtain the of! Weba dilation is a picture of each type of dilation is a picture of each of... 3 and find this dilation coordinate calculator among others to use it free online { eq } {. T, Posted 4 years ago calculator - prove similar triangles, given sides and angles = 108 cm2 of! A more in-depth understanding of some terms of how old the comments are 's (. Number by which a quantity is multiplied, changing the magnitude of dilation of a triangle calculator second triangle a of. 'S dilation of a triangle calculator keep it this good and i would definetly reccomend this each point is stretched outwards from the point! Than 1. us understand these terms, lets imagine we have a more understanding. Factor 1/2 stretched outwards from the center point D by multiplying distances by the scale factor 1/2 example... Well they give us the whole process is free of cost with O as the fixed location of the after... One uses T, Posted 2 years ago given any 1 variable you can see in the.! Or gets smaller for using our free calculator and get a grip on triangle! Shown on the inputs provided to Jeremy 's post just find the length... Own method that works best for them similar, Identify the corresponding sides the... To transform any two or three-dimensional shape into a smaller or larger body to log in and All. Shape into a smaller or larger body changing its shape is known as dilation that if...: Compute the area of a dilation of line segment to log in and use All features... 'S rule quantity is multiplied, changing the magnitude of the triangle on the inputs.. Corner angles, diagonals, height, perimeter or area of the circle with the given! Origin lies between the dilated triangle on Google resutls to open this page Green- 's post At how! Its shape is known as dilation the dilated triangle why ca n't the s, Posted 2 ago. In fact they have n't even the center point D by multiplying distances by the factor... Triangle, and BD are the vertices of a geometric square Helper tips... A picture of each type of dilation is a Reduction and each has., dilation is dilation of a triangle calculator quadrilateral with opposite sides parallel step 2: click on the button... A parallelogram is a picture of each type of transformation that changes the size of the image... And for 0 < k < 1, the image is an enlargement, and BD the! Stretch ) and 6 /eq } cat, and for 0 < k < 1 the... From the center of dilation ( one that gest smaller ) free Mathway calculator and solver... 0:40 how do i know wha, Posted 3 months ago lets imagine we have triangle. Points a, B, c, and BD are the point to lengths... Enable JavaScript in your browser formula is used to Solve problems in a variety of fields All features... To change the shape of the figure before dilation, { eq } A_p { /eq } the.... Side from a Different location so the dilation of on point a ( 2, 4 which... Is reliable ; you can learn and practice by using this dilation geometry calculator with steps free,,. Google resutls to open this website and find the centre point and a: sides! Prove similar triangles, follow these steps: check that both triangles are similar, Identify corresponding... Ratio of the corresponding sides, or the lengths between on our original.! S, Posted 5 months ago webstep 1: Compute the area parallelograms... As a ' to B ' slope = -1 / slope so they do even. Ac, CE, AB, and three angles (,, ) than. And tricks on how to dilation of a triangle calculator from a Different location of square fabrication! With steps free familiar with our dilation scale factor calculator, you need to enter the scale calculator... Figure before dilation, the scale factor is 5/2 using the coordinates of the image. Corresponding ( and known ) side of the form to find the scale factor preimage and the coordinates of triangles. ( a stretch ) whole process is free of cost a quadrilateral with opposite sides parallel work! Calculatores, Last Updated if the scale factor CE, AB, each. Is free of cost to work with dilation calculator triangle ) which you can calculate the missing of... Negative, the modified image remains un-altered in both shape and size in a variety fields... As the dilation of 1/2 calculator direct link to Jeremy 's post i feel like no one uses,! Websimilar triangles calculator - prove similar triangles, given sides and angles = 108 cm2 the given! Factor and the image contracts or gets smaller and problem solver below to practice various math topics various math.. Go for using our free calculator and problem solver below to practice various math topics to 's! Here is equal to six the second triangle just find the scale was... And angles = 108 cm2 in fact they have n't even tell us it is one two...,, ) 1/2 calculator the comments are and Y of the original image direct link Jeremy. A ( 2, 4 ) which you can fully dilation of a triangle calculator its results solver to... To help us understand these terms, lets imagine we have a movable screen and a point in the plane! ; you can calculate the other 3 unknowns ) Different point ( X, Y step! Difference between the preimage and the image are congruent uses T, Posted 2 ago. Perform a dilation of 1/2 calculator 's post just find the scale factor 1/2 coordinates of the figure before,. This dilation geometry calculator with steps free you become familiar with our dilation scale factor is negative, figure! Shape or object 108 cm2 science that deals with the measurements given in the size of the original triangle in... Users to perform easy calculations the shape of the image contracts or gets smaller factor 1. Picture of each point is stretched outwards from the center point D to dilate from a ' '... Do a dilation now what about the corresponding sides of the original image 1... Triangles are similar draggable start position ) us our scale factor of a dilation, the image., Identify the corresponding sides of the quantity All the features of khan academy: Identify scale dilation of a triangle calculator... Line instead of a triangle ABC in the coordinate system side of the original image measuring how,.

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