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 $S(-2,-2)$: $S'=(-2,2)$.
For point $T(-5,-6)$: $T'=(-6,5)$.
For point $U(-6,-6)$: $U'=(-6,6)$.
For point $V(-6,-5)$: $V'=(-5,6)$.

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:

The coordinates of the pre - image are $S(-2,-2),T(-5,-6),U(-6,-6),V(-6,-5)$.
The coordinates after 90 - degree clockwise rotation about the origin are $S'(-2,2),T'(-6,5),U'(-6,6),V'(-5,6)$.
The coordinates after translation $(x,y)\to(x + 8,y + 1)$ are $S''(6,3),T''(2,6),U''(2,7),V''(3,7)$.