Question

in exercises 17 and 19, graph $\triangle pqr$ with vertices $p(-2, 3)$, $q(1, 2)$, and $r(3, -1)$ and its image after the translation. (see example 4.)

1. $(x, y) \to (x + 4, y + 6)$
2. $(x, y) \to (x - 2, y - 5)$

Explanation:

Step1: Solve for Exercise 17 vertices

Apply $(x,y)\to(x+4,y+6)$:

• $P'(-2+4, 3+6)=(2,9)$
• $Q'(1+4, 2+6)=(5,8)$
• $R'(3+4, -1+6)=(7,5)$

Step2: Solve for Exercise 19 vertices

Apply $(x,y)\to(x-2,y-5)$:

• $P''(-2-2, 3-5)=(-4,-2)$
• $Q''(1-2, 2-5)=(-1,-3)$
• $R''(3-2, -1-5)=(1,-6)$

Answer:

For Exercise 17:

Image vertices: $P'(2, 9)$, $Q'(5, 8)$, $R'(7, 5)$
(Plot these points and connect them to form the translated triangle on the first grid, along with the original $\triangle PQR$)

For Exercise 19:

Image vertices: $P''(-4, -2)$, $Q''(-1, -3)$, $R''(1, -6)$
(Plot these points and connect them to form the translated triangle on the second grid, along with the original $\triangle PQR$)