Question

which sequence of transformations will map triangle a onto its congruent image, triangle b? a a reflection over the x - axis, then a reflection over the y - axis b a translation 8 units down, then a reflection over the y - axis c a reflection over the x - axis, then a translation 6 units to the left d a rotation 90° clockwise about the origin, then a translation 6 units to the left

Explanation:

Step1: Analyze option A

A reflection over the x - axis changes the sign of the y - coordinates. A reflection over the y - axis changes the sign of the x - coordinates. This will not map triangle A to triangle B.

Step2: Analyze option B

A translation 8 units down subtracts 8 from the y - coordinates. A reflection over the y - axis changes the sign of the x - coordinates. This will not map triangle A to triangle B.

Step3: Analyze option C

A reflection over the x - axis changes (x,y) to (x, - y). Then a translation 6 units to the left changes (x, - y) to (x - 6,-y). This will map triangle A to triangle B.

Step4: Analyze option D

A 90 - degree clockwise rotation about the origin changes (x,y) to (y, - x). Then a translation 6 units to the left changes (y, - x) to (y - 6,-x). This will not map triangle A to triangle B.

Answer:

C. a reflection over the x - axis, then a translation 6 units to the left