Question

△cde was rotated 90° clockwise around the origin to form △cde. △cde was dilated using a scale factor of 1/2 with a center of dilation at the origin. the result is △cde, shown in the coordinate plane. what are the coordinates of △cde? c(4, 6); d(2, 2); e(-2, 6) c(4, -6); d(2, -2); e(-2, -6) c(6, -4); d(2, -2); e(6, 2) c(-6, 4); d(-2, 2); e(-6, -2)

Explanation:

Step1: Reverse the dilation

To reverse the dilation with a scale - factor of $\frac{1}{2}$ centered at the origin, we multiply the coordinates of $\triangle C''D''E''$ by 2. Let the coordinates of $C''(2,3)$, $D''(1,1)$, $E''(- 1,3)$. After reversing the dilation, the coordinates of $\triangle C'D'E'$ are $C'(4,6)$, $D'(2,2)$, $E'(-2,6)$.

Step2: Reverse the rotation

The rule for a $90^{\circ}$ clock - wise rotation about the origin is $(x,y)\to(y, - x)$. To reverse a $90^{\circ}$ clock - wise rotation, we use the rule $(x,y)\to(-y,x)$.
For $C'(4,6)$, reversing the rotation gives $C( - 6,4)$.
For $D'(2,2)$, reversing the rotation gives $D(-2,2)$.
For $E'(-2,6)$, reversing the rotation gives $E(-6,-2)$.

Answer:

$C(-6,4);D(-2,2);E(-6,-2)$