Question

rule:

1. triangle ( xyz ) with vertices ( x(-3,7), y(-2,1) ),

and ( z(-5,2) ).
(a) reflection: in the ( x )-axis
(b) translation: ( (x, y)
ightarrow(x+9, y+2) )

Explanation:

Step1: Reflection over the x - axis

The rule for reflection over the x - axis is \((x,y)\to(x, - y)\).
For point \(X(-3,7)\), after reflection \(X'( - 3,-7)\).
For point \(Y(2,1)\), after reflection \(Y'(2, - 1)\).
For point \(Z(-5,2)\), after reflection \(Z'(-5, - 2)\).

Step2: Translation \((x,y)\to(x + 9,y+2)\)

For \(X'(-3,-7)\):
\(x=-3 + 9=6\), \(y=-7 + 2=-5\), so \(X''(6,-5)\)
For \(Y'(2,-1)\):
\(x=2 + 9 = 11\), \(y=-1+2 = 1\), so \(Y''(11,1)\)
For \(Z'(-5,-2)\):
\(x=-5 + 9=4\), \(y=-2 + 2=0\), so \(Z''(4,0)\)

Answer:

\(X'(6,-5)\), \(Y'(11,1)\), \(Z'(4,0)\)