Question

answer all parts of the question on the graph to the right. plot the pre - image and label it appropriately. make sure to show the transformations using different colors and labeling them appropriately. show the line of reflection when reflecting.
. plot the pre - image. quadrilateral stuv: s(-2, -2), t(-5, -6), u(-6, -6), v(-6, -5)
. then, rotate the quadrilateral 90° clockwise about the origin creating image stuv.
. then, translate stuv (x, y)→(x + 8, y + 1) creating image stuv

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$.
For point S(-2,-2), after rotation: $S'=(-2,2)$.
For point T(-5,-6), after rotation: $T'=(-6,5)$.
For point U(-6,-6), after rotation: $U'=(-6,6)$.
For point V(-6,-5), after rotation: $V'=(-5,6)$.

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 8,y + 1)$.
For $S'(-2,2)$: $S''=(-2+8,2 + 1)=(6,3)$.
For $T'(-6,5)$: $T''=(-6+8,5 + 1)=(2,6)$.
For $U'(-6,6)$: $U''=(-6+8,6 + 1)=(2,7)$.
For $V'(-5,6)$: $V''=(-5+8,6 + 1)=(3,7)$.

Answer:

Pre - image points: S(-2,-2), T(-5,-6), U(-6,-6), V(-6,-5)
Image after rotation: S'(-2,2), T'(-6,5), U'(-6,6), V'(-5,6)
Image after translation: S''(6,3), T''(2,6), U''(2,7), V''(3,7)