Question

graph $\triangle pqr$ with vertices $p(1,2)$, $q(3,1)$, and $r(1, -3)$ and its image after a dilation with a scale factor of $-2$.

Explanation:

Step1: Recall dilation rule

For a dilation with scale factor \( k \), the coordinates \((x,y)\) transform to \((k x, k y)\). Here, \( k=-2 \).

Step2: Dilate point \( P(1,2) \)

Multiply each coordinate by \(-2\): \( P' = (-2\times1, -2\times2) = (-2, -4) \)

Step3: Dilate point \( Q(3,1) \)

Multiply each coordinate by \(-2\): \( Q' = (-2\times3, -2\times1) = (-6, -2) \)

Step4: Dilate point \( R(1,-3) \)

Multiply each coordinate by \(-2\): \( R' = (-2\times1, -2\times(-3)) = (-2, 6) \)

To graph:

• Plot original points \( P(1,2) \), \( Q(3,1) \), \( R(1,-3) \) and connect to form \( \triangle PQR \).
• Plot dilated points \( P'(-2,-4) \), \( Q'(-6,-2) \), \( R'(-2,6) \) and connect to form the image triangle.

Answer:

Original vertices: \( P(1,2) \), \( Q(3,1) \), \( R(1,-3) \); Dilated vertices: \( P'(-2,-4) \), \( Q'(-6,-2) \), \( R'(-2,6) \) (Graph by plotting these points and connecting them for each triangle).