Question

1. rectangle abcd plotted at a(3,2), b(6,2), c(6,9) and d(3,9) is to be rotated 90° (center of rotation is the origin).

a) plot the image of abcd under this rotation and label it abcd. state the new coordinates: a = ____ b = __ c = __ d = ____
b) were the angle measures preserved during this rotation? describe how you made your decision.
c) are rotations rigid transformations? ______ explain.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Find coordinates of $A'$

For $A(3,2)$, using the rule $(x,y)\to(-y,x)$, we have $A'=(- 2,3)$.

Step3: Find coordinates of $B'$

For $B(6,2)$, using the rule $(x,y)\to(-y,x)$, we have $B'=(-2,6)$.

Step4: Find coordinates of $C'$

For $C(6,9)$, using the rule $(x,y)\to(-y,x)$, we have $C'=(-9,6)$.

Step5: Find coordinates of $D'$

For $D(3,9)$, using the rule $(x,y)\to(-y,x)$, we have $D'=(-9,3)$.

Step6: Answer part b

Yes, angle measures are preserved. Rotations are rigid transformations. Rigid transformations preserve shape and size, including angle measures.

Step7: Answer part c

Yes, rotations are rigid transformations. Rigid transformations preserve distance and angle measures. A rotation only changes the orientation of a figure in the plane, not its size or shape.

Answer:

a) $A'=(-2,3)$; $B'=(-2,6)$; $C'=(-9,6)$; $D'=(-9,3)$
b) Yes. Rotations are rigid transformations which preserve angle measures.
c) Yes. They preserve distance and angle measures.