Question

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

Explanation:

Step1: Recall rigid - transformation rules

Rigid transformations include translations (shifts) and rotations. A counter - clockwise rotation of 90° has the transformation rule $(x,y)\to(-y,x)$. A translation of $a$ units left and $b$ units up has the rule $(x,y)\to(x - a,y + b)$.

Step2: Analyze the order of operations

If we first rotate a point $(x,y)$ counter - clockwise by 90°, we get $(-y,x)$. Then if we shift this new point 3 units left and 5 units up, we get $(-y-3,x + 5)$. If we first shift $(x,y)$ 3 units left and 5 units up, we get $(x - 3,y + 5)$, and then rotating 90° counter - clockwise gives $(-(y + 5),x - 3)$.

Step3: Check the options

A 90° counter - clockwise rotation followed by a translation of 3 units left and 5 units up is a valid sequence of rigid transformations for congruent figures. A 270° clockwise rotation is equivalent to a 90° counter - clockwise rotation. But the order of operations matters. The correct order is first rotation then translation to match the general behavior of rigid transformations for congruent figures in a coordinate plane.

Answer:

B. $ABCD$ was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.