Question

figures t and t are congruent. what sequence of transformations maps figure t to figure t?
solution
triangles r and s are congruent. which sequence of transformations can you perform on triangle r to show this?
a rotate triangle r 90° clockwise around the origin.
b rotate triangle r 180° clockwise around the origin.
c rotate triangle r 90° clockwise around the origin. then translate the image right 3 units.
d rotate triangle r 180° clockwise around the origin. then reflect the image across the y - axis.

Explanation:

Step1: Recall rotation rules

A 90 - degree clock - wise rotation around the origin has the rule $(x,y)\to(y, - x)$. A 180 - degree clock - wise rotation around the origin has the rule $(x,y)\to(-x,-y)$. A reflection across the y - axis has the rule $(x,y)\to(-x,y)$.

Step2: Analyze option A

If we rotate triangle R 90° clockwise around the origin, the orientation and position of the triangle will not match triangle S.

Step3: Analyze option B

If we rotate triangle R 180° clockwise around the origin, the resulting triangle will have the correct orientation and position to match triangle S.

Step4: Analyze option C

A 90 - degree clockwise rotation followed by a translation right 3 units will not map triangle R to triangle S.

Step5: Analyze option D

A 180 - degree clockwise rotation followed by a reflection across the y - axis will not map triangle R to triangle S.

Answer:

B. Rotate triangle R 180° clockwise around the origin.