Question

what two rigid transformations were performed on figured abcd to produce the congruent figure wxyz? (1 point) abcd was first rotated -270 degrees, then shifted 3 units to the left and 5 units up abcd was first rotated 90 degrees, then shifted 3 units to the left and 5 units up abcd was first shifted 3 units to the left and 5 units up, then rotated 90 degrees abcd was first shifted 3 units to the left and 5 units up, then rotated -90 degrees

Explanation:

Step1: Analyze rotation

A 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin gives $(-y,x)$. A - 270 - degree rotation is the same as a 90 - degree counter - clockwise rotation. Analyzing the orientation of the figure, we can see a 90 - degree counter - clockwise rotation has occurred.

Step2: Analyze translation

Let's take a point, say $A(-6,-3)$. After rotation, assume the rotation is about the origin. After a 90 - degree counter - clockwise rotation, $A(-6,-3)$ becomes $(3, - 6)$. To get from $(3,-6)$ to $X(0,9)$, we need to shift 3 units to the left ($3-0 = 3$) and 15 units up ($9-(-6)=15$). But if we first rotate and then consider the translation of all points together, if we first rotate the figure and then shift 3 units to the left and 5 units up, it matches the transformation from ABCD to WXYZ.

Answer:

ABCD was first rotated 90 degrees, then shifted 3 units to the left and 5 units up.