Lesson 5
More Dilations
Let’s look at dilations in the coordinate plane.
Problem 1
Quadrilateral \(ABCD\) is dilated with center \((0,0)\), taking \(B\) to \(B'\). Draw \(A'B'C'D'\).
![A quadrilateral, A, negative 2 comma 3, B, 3 comma 1, C, 1 comma negative 1, D, negative 3 comma negative 2. Another point, B prime, 6 comma 2.](https://cms-im.s3.amazonaws.com/kMSntvCPDjZzU1hHntfmoCC5?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.10.3.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.10.3.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025610Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3433981e2084bf7d228cfab1f8b058cdd9bd20a2dba221906b46f77c42155976)
Problem 2
Triangles \(B\) and \(C\) have been built by dilating Triangle \(A\).
![Three triangles, 2 of which are dilations of the first. Please ask for further assistance.](https://cms-im.s3.amazonaws.com/QhQZu4dyyfAhnaAfJWh41pHH?response-content-disposition=inline%3B%20filename%3D%228.2.A5.newPP.Image.01%20%25281%2529.png%22%3B%20filename%2A%3DUTF-8%27%278.2.A5.newPP.Image.01%2520%25281%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025610Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=72b470201b8323a10c31a265070759b23094baec10babadde64e1e8691af4f16)
- Find the center of dilation.
- Triangle \(B\) is a dilation of \(A\) with approximately what scale factor?
- Triangle \(A\) is a dilation of \(B\) with approximately what scale factor?
- Triangle \(B\) is a dilation of \(C\) with approximately what scale factor?
Problem 3
Here is a triangle.
- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor 2. Label this triangle \(A’B’C’\).
- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor \(\frac{1}{2}\). Label this triangle \(A’’B’’C’’\).
- Is \(A’’B’’C’’\) a dilation of triangle \(A’B’C’\)? If yes, what are the center of dilation and the scale factor?
![Coordinate plane, x, negative 7 to 8, y, negative 6 to 6. A triangle, A, 4 comma negative 2, B, negative 2 comma negative 2, C, negative 2 comma 2.](https://cms-im.s3.amazonaws.com/GxLShQ5qMCVtpj9oTygKTaRj?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.22.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025610Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=621b6f9f845f0997768aae509ea5aa39a0e13c9ef838ea47e386d270130d9a9a)
Problem 4
Triangle \(DEF\) is a right triangle, and the measure of angle \(D\) is \(28^\circ\). What are the measures of the other two angles?