Question

which series of transformations shows that triangle a is congruent to triangle b? two grid graphs with triangles labeled triangle a (brown) and triangle b (green), axes from -8 to 8 a. reflect triangle a over the y - axis and translate it 2 units up. b. reflect triangle a over the y - axis, rotate it 90° counterclockwise about the origin, and translate it 5 units to the right. c. reflect triangle a over the x - axis, translate it 4 units to the right, and reflect it over the y - axis. d. reflect triangle a over the y - axis, translate it 5 units to the right, and rotate it 90° counterclockwise about the origin.

Explanation:

Step1: Identify vertices of Triangle A

Assume vertices of A: (1,2), (3,7), (4,4)

Step2: Apply option B transformations

• Reflect over y-axis: (-1,2), (-3,7), (-4,4)
• Rotate 90° counterclockwise: (-2,-1), (-7,-3), (-4,-4)
• Translate 5 right: (3,-1), (2,-3), (1,-4) → matches Triangle B's position.

Other options fail to map A to B.

Answer:

B. Reflect triangle A over the y-axis, rotate it 90° counterclockwise about the origin, and translate it 5 units to the right.