Question

in the diagram, pentagons qrstu and qrstu are congruent. which sequence of transformations can be performed on figure qrstu to show that the figures are congruent? translate figure qrstu 6 units right. then reflect the image across the x -axis. rotate figure qrstu 90° clockwise around the origin. then translate the image 6 units right. rotate figure qrstu 90° clockwise around the origin. then reflect the image across the y -axis. reflect figure qrstu across the x -axis. then rotate the image 90° clockwise around the origin.

Explanation:

Step1: Analyze rotation rule

A 90 - degree clock - wise rotation around the origin has the rule $(x,y)\to(y, - x)$.

Step2: Analyze translation

Translating 6 units right means adding 6 to the x - coordinate of each point.

Step3: Check the result

Applying these transformations on $QRSTU$ will map it onto $Q''R''S''T''U''$.

Answer:

B. Rotate figure $QRSTU$ 90° clockwise around the origin. Then translate the image 6 units right.