Question

1. rectangle defg with vertices d(-2, 7), e(2, 3), f(0, 1), and g(-4, 5): a) translation along the rule (x, y)→(x + 6,y - 8)→ b) reflection in the y - axis d e d(, ) f e(, ) f(, ) g g(, )

Explanation:

Step1: Apply the translation rule

For point \(D(-2,7)\), using the rule \((x,y)\to(x + 6,y-8)\), we have \(x=-2\), \(y = 7\). Then \(x'=-2+6 = 4\) and \(y'=7 - 8=-1\), so \(D'=(4,-1)\). For \(E(2,3)\), \(x = 2\), \(y=3\), \(x'=2 + 6=8\), \(y'=3-8=-5\), so \(E'=(8,-5)\). For \(F(0,1)\), \(x = 0\), \(y = 1\), \(x'=0+6 = 6\), \(y'=1-8=-7\), so \(F'=(6,-7)\). For \(G(-4,5)\), \(x=-4\), \(y = 5\), \(x'=-4+6 = 2\), \(y'=5-8=-3\), so \(G'=(2,-3)\).

Step2: Apply the reflection rule

The rule for reflection in the \(y -\)axis is \((x,y)\to(-x,y)\). For \(D'(4,-1)\), the new point \(D''=(-4,-1)\). For \(E'(8,-5)\), the new point \(E''=(-8,-5)\). For \(F'(6,-7)\), the new point \(F''=(-6,-7)\). For \(G'(2,-3)\), the new point \(G''=(-2,-3)\).

Answer:

\(D''(-4,-1)\), \(E''(-8,-5)\), \(F''(-6,-7)\), \(G''(-2,-3)\)