Question

example 4
describe each dilation. then write a coordinate rule to represent the dilation.

1. $\triangle jkp$ is the image of $\triangle jkp$.
2. $\triangle dfg$ is the image of $\triangle dfg$.

Explanation:

Step1: Identify coordinates for #12

First, pick vertices of $\triangle JKP$ and $\triangle J'K'P'$:
$J(2,2), K(4,2), P(3,0)$; $J'(2,4), K'(4,4), P'(3,1)$

Step2: Find scale factor for #12

Compare corresponding coordinates:
For $J$ to $J'$: $\frac{4}{2}=2$, $\frac{2}{2}=1$ (x stays, y doubles). Same for all vertices.
Dilation center: $(0,0)$ (origin, since scaling is from origin).
Coordinate rule: $(x,y)\to(x,2y)$

Step3: Identify coordinates for #13

Pick vertices of $\triangle DFG$ and $\triangle D'F'G'$:
$D(-1,0), F(3,-2), G(0,2)$; $D'(-2,0), F'(6,-4), G'(0,4)$

Step4: Find scale factor for #13

Compare corresponding coordinates:
For $D$ to $D'$: $\frac{-2}{-1}=2$, $\frac{0}{0}=1$; for $F$ to $F'$: $\frac{6}{3}=2$, $\frac{-4}{-2}=2$; for $G$ to $G'$: $\frac{0}{0}=1$, $\frac{4}{2}=2$.
Dilation center: $(0,0)$ (origin).
Coordinate rule: $(x,y)\to(2x,2y)$

Answer:

1. Dilation: A vertical stretch (scale factor 2, center at origin) that maps $\triangle JKP$ to $\triangle J'K'P'$.

Coordinate Rule: $(x,y)\to(x,2y)$

1. Dilation: A dilation with scale factor 2, center at origin, that maps $\triangle DFG$ to $\triangle D'F'G'$.

Coordinate Rule: $(x,y)\to(2x,2y)$