Question

1. triangle ( gjh ) with vertices ( g(-1,6), h(-1,3) ), and ( i(-6,6) ):

(a) translation: ( (x, y)
ightarrow(x+7, y - 5) )
(b) reflection: in the line ( y=-3 )
( g^{prime}(quad,quad) )
( h^{prime}(quad,quad) )
( i^{prime}(quad,quad) )

Explanation:

Step1: Apply the translation rule

The translation rule is \((x,y)\to(x + 7,y-5)\).
For point \(G(-1,6)\):
\(x=-1,y = 6\)
\(x+7=-1 + 7=6\)
\(y - 5=6-5 = 1\)
For point \(H(-1,3)\):
\(x=-1,y = 3\)
\(x+7=-1+7 = 6\)
\(y-5=3 - 5=-2\)
For point \(I(-6,6)\):
\(x=-6,y = 6\)
\(x+7=-6+7 = 1\)
\(y-5=6-5 = 1\)

Step2: Apply the reflection rule

The reflection rule over the line \(y=-3\) is \((x,y)\to(x,-6 - y)\)
For \(G'(6,1)\):
\(x = 6,y=1\)
\(x\) remains \(6\), \(y=-6 - 1=-7\)
For \(H'(6,-2)\):
\(x = 6,y=-2\)
\(x\) remains \(6\), \(y=-6-(-2)=-4\)
For \(I'(1,1)\):
\(x = 1,y = 1\)
\(x\) remains \(1\), \(y=-6 - 1=-7\)

Answer:

\(G'(6,-7)\)
\(H'(6,-4)\)
\(I'(1,-7)\)