Question

use your knowledge of dilations to answer each question below. justina needs to dilate triangle abc using a scale factor of 1.5. use the graph to answer 1-3. 1. record the coordinates of justina’s pre - image and image. pre - image image a a b b c c 2. draw a’b’c’ on the graph. 3. write a rule to represent the dilation.

Explanation:

Step1: Find the scale factor relationship

For a dilation, if the pre - image point is \((x,y)\) and the image point is \((x',y')\), the rule is \((x,y)\to(kx,ky)\), where \(k\) is the scale factor. Given \(A(- 2,2)\) and \(A'(-3,3)\), we can find \(k\) by calculating \(k=\frac{x'}{x}=\frac{-3}{-2}=1.5\) or \(k = \frac{y'}{y}=\frac{3}{2}=1.5\).

Step2: Write the general rule

The general rule for the dilation is \((x,y)\to(1.5x,1.5y)\).

Answer:

\((x,y)\to(1.5x,1.5y)\)