Question

1. consider $\triangle pqr$ in the coordinate plane.

a. what are the coordinates of the images of vertices $p$, $q$, and $r$ under a dilation centered at the origin with scale factor $1.5?$
b. graph and label the image of $\triangle pqr$ under the same dilation.

Explanation:

Step1: Find original coordinates

From the graph, \( P(-5, 2) \), \( Q(-4, 4) \), \( R(-2, 4) \).

Step2: Apply dilation formula

Dilation centered at origin: \((x,y)\to(1.5x,1.5y)\).
For \( P \): \( 1.5\times(-5)= -7.5 \), \( 1.5\times2 = 3 \) → \( P'(-7.5, 3) \).
For \( Q \): \( 1.5\times(-4)= -6 \), \( 1.5\times4 = 6 \) → \( Q'(-6, 6) \).
For \( R \): \( 1.5\times(-2)= -3 \), \( 1.5\times4 = 6 \) → \( R'(-3, 6) \).

Answer:

a. \( P'(-7.5, 3) \), \( Q'(-6, 6) \), \( R'(-3, 6) \)
b. (Graphing: Plot \( P'(-7.5, 3) \), \( Q'(-6, 6) \), \( R'(-3, 6) \) and connect them to form \( \triangle P'Q'R' \))