Question

triangle xyz with vertices x(-3, 7), y(-2, 1), and z(-5, 2): (a) reflection in the x - axis (b) translation: (x, y)→(x + 9, y + 2)

Explanation:

Step1: Reflection in x - axis rule

The rule for reflection in the x - axis is $(x,y)\to(x, - y)$.
For point $X(-3,7)$, after reflection in the x - axis, $X_1=(-3,-7)$.
For point $Y(-2,1)$, after reflection in the x - axis, $Y_1=(-2,-1)$.
For point $Z(-5,2)$, after reflection in the x - axis, $Z_1=(-5,-2)$.

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 9,y + 2)$.
For $X_1(-3,-7)$, $X'=(-3 + 9,-7+2)=(6,-5)$.
For $Y_1(-2,-1)$, $Y'=(-2 + 9,-1 + 2)=(7,1)$.
For $Z_1(-5,-2)$, $Z'=(-5 + 9,-2 + 2)=(4,0)$.

Answer:

$X'(6,-5),Y'(7,1),Z'(4,0)$