Question

question #3 g.gsr.3.3 identify the sequence of transformations that maps △a onto its image △b. a. reflection over x - axis and translation 2 units down b. reflection over the y - axis and translation 2 units down c. translation 2 units down and 90° cw rotation about the origin d. translation 12 units right and translation 2 units down

Explanation:

Step1: Analyze option a

A reflection over the x - axis changes the sign of the y - coordinates of the vertices of triangle A. Then a translation 2 units down further decreases the y - coordinates by 2. This does not map triangle A onto triangle B.

Step2: Analyze option b

A reflection over the y - axis changes the sign of the x - coordinates of the vertices of triangle A. Then a translation 2 units down changes the y - coordinates. This does not map triangle A onto triangle B.

Step3: Analyze option c

A 90° clock - wise (CW) rotation about the origin has the transformation rule \((x,y)\to(y, - x)\). A translation 2 units down then changes the y - coordinate. This does not map triangle A onto triangle B.

Step4: Analyze option d

A translation 12 units right changes the x - coordinates of the vertices of triangle A by adding 12. Then a translation 2 units down changes the y - coordinates by subtracting 2. This maps triangle A onto triangle B.

Answer:

d. Translation 12 units right and translation 2 units down