Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their

Essential Question: What is a dilation and how do you dilate a figure?Assessment: Students will demonstrate in writing through practice problems in their notebooks

Warm Up 1) Are the following shapes congruent? 2) If so, what type of transformation is occurring?

DILATIONSEssential Question: What is a dilation and how do

you dilate a figure?Assessment: Students will demonstrate in writing

through practice problems in their notebooks


Prior KnowledgeDistance Formula


What is a Dilation? A dilation is a transformation that

produces an image that is the same shape as the original, but is a different size.

A dilation reduces or enlarges the original figure.


What is a Dilation? The description of a dilation includes the

scale factor (or ratio) and the center of the dilation.The center of the dilation is a fixed point in

the plane about which all points are reduced or enlarged. It is the only fixed point under a dilation.


Properties of a Dilation 1) Angle measures remain the same

2) Parallel lines remain parallel.

3) Points that start on the same line stay

on the same line.

4) Midpoints remain the same.

5) Letter ordering remains the same.


Scale Factor To find the scale factor (denoted k) of a dilation find

the coordinates of two points in the pre-image and the coordinates of the two corresponding points on the image.

Find the length of the segments created by these points. (Insert into notes)

Divide the length from the image by the length from the pre-image.If then the image is smaller than the preimage.If then the image is larger than the preimage.


ExampleFind the scale factor of the image


ExamplesFind the scale factor in each of the images


Dilating about a Point If you are asked to dilate a figure containing the vertex

(a, b) by a scale factor of k about the point (m, n).1. Find the horizontal distance from a to m.2. Multiply this horizontal distance by k.3. Add the answer from step 2 to m and this gives you the x-

coordinate of your dilation.4. Find the vertical distance from b to n.

○ This will be positive if (a, b) is above (m, n) and will be negative if (a, b) is below.

5. Multiply this vertical distance by k.6. Add the answer from step 5 to n and this gives you the y-

coordinate of your dilation.7. Plot your new point.8. Repeat from all other vertices.


ExamplePerform a dilation of the line segment AB centered at P with a scale factor of 2.


ExamplePerform a dilation of the line segment centered at (-5, -2) with a scale factor of .


ExampleLine segment ST and point P are shown below. The line segment undergoes a dilation by a scale factor of 1.5 through center P to produce line segment S'T'.

Which of the following equations are true? Select all that apply.

A S’T’=5.5

B S’T’=6

C

D


ExampleGuillermo claims that a dilation with a scale factor of 3 will triple the perimeter of figure. His friend asks Guillermo to show this by using the figure below where A is (-4, -2), B is (-4, 2) and C is (-1, 2).

Part A: What is the perimeter of ΔABC?

Part B: Apply a dilation with a scale factor of 3 about point B to find the perimeter of the new image. Is Guillermo’s claim supported?


In the figure, the smaller shape is a dilation of the larger shape. What is the scale factor of the dilation, and what is the center of the dilation?

A scale factor: 3 ; center: (1,3) B scale factor: 2 ; center: (−1,1) C scale factor: 2 ; center:(0,0) D scale factor: 112 ; center: (1,3) E scale factor: 1 ; center: (0,0) F scale factor: 12 ; center: (1,3) G scale factor: 12 ; center: (0,0) H scale factor: 13 ; center: (−1,1)


In the figure, the smaller shape is a dilation of the larger shape. What is the scale factor of the dilation, and what is the center of the dilation?

A scale factor: 3 ; center: (3,0) B scale factor: 3 ; center: (112,−3) C scale factor: 2 ; center: (0,0) D scale factor: 112 ; center: (112,−3) E scale factor: 12 ; center: (0,0) F scale factor: 12 ; center: (12,−1) G scale factor: 13 ; center: (0,0) H scale factor: 14 ; center: (12,−1)


In the figure, the larger shape is a dilation of the smaller shape. What is the scale factor of the dilation, and what is the center of the dilation?

A scale factor: 3; center: (3,0) B scale factor: 3; center: (0,0) C scale factor: 2; center: (12,−1) D scale factor: 112 ; center: (112,−3) E scale factor: 12 ; center: (0,0) F scale factor: 12 ; center: (3,0) G scale factor: 13 ; center: (0,0)


Essential Question

What is a dilation and how do you dilate a figure?

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Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their