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. c) are reflections rigid transformations? explain.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.
For point $A(3,2)$:
$A'=(-2,3)$
For point $B(6,2)$:
$B'=(-2,6)$
For point $C(6,9)$:
$C'=(-9,6)$
For point $D(3,9)$:
$D'=(-9,3)$

Step2: Analyze angle preservation

Rotation is a rigid transformation. Rigid transformations preserve side lengths and angle measures. Since rotation only changes the orientation of the figure in the coordinate plane and does not stretch or compress it, the angle measures of rectangle $ABCD$ are preserved during the 90 - degree rotation about the origin.

Step3: Define rigid transformation

A rigid transformation is a transformation that preserves distance and angle measures. Rotations preserve the shape and size of a figure. The distance between any two points in the pre - image is the same as the distance between their corresponding points in the image, and the angle measures are also the same. So, rotations are rigid transformations. Also, reflections are rigid transformations because they also preserve distance and angle measures. A reflection flips a figure over a line of reflection without changing its size or shape.

Answer:

a) $A'=(-2,3)$, $B'=(-2,6)$, $C'=(-9,6)$, $D'=(-9,3)$
b) Yes. Rotation is a rigid transformation which preserves angle measures.
c) Yes. Rotations preserve distance and angle measures. Also, reflections are rigid transformations as they preserve distance and angle measures.