Question

directions: graph and label each figure and its image under the sequence of transformations. give the coordinates of the image.

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(_,_)
f(_,_)
g(_,_)

Explanation:

Step1: Apply translation

For a translation \((x,y)\to(x + 6,y-8)\):

• For \(D(-2,7)\): \(x=-2+6 = 4\), \(y=7 - 8=-1\), so \(D'(4,-1)\)
• For \(E(2,3)\): \(x=2+6 = 8\), \(y=3 - 8=-5\), so \(E'(8,-5)\)
• For \(F(0,1)\): \(x=0+6 = 6\), \(y=1 - 8=-7\), so \(F'(6,-7)\)
• For \(G(-4,5)\): \(x=-4+6 = 2\), \(y=5 - 8=-3\), so \(G'(2,-3)\)

Step2: Apply reflection in the \(y\) - axis

The rule for reflection in the \(y\) - axis is \((x,y)\to(-x,y)\)

• For \(D'(4,-1)\): \(x=-4\), \(y=-1\), so \(D''(-4,-1)\)
• For \(E'(8,-5)\): \(x=-8\), \(y=-5\), so \(E''(-8,-5)\)
• For \(F'(6,-7)\): \(x=-6\), \(y=-7\), so \(F''(-6,-7)\)
• For \(G'(2,-3)\): \(x=-2\), \(y=-3\), so \(G''(-2,-3)\)

Answer:

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