Question

A sequence of transformations maps triangle ABC to triangle A'B'C. The sequence of transformations that maps triangle ABC onto triangle A'B'C is [Blank] followed by [Blank].

Options:
A) Rotation 180 degrees counterclockwise about the origin, Reflection across the y-axis
B) Rotation 90 degrees clockwise about the origin, Translation 4 units to the right
C) Reflection across the line x = -3, Reflection across the line y = -3
D) Reflection across the line y = x, Reflection across the line y = -x

Answer 1

The correct sequence of transformations that maps triangle ABC to triangle A'B'C is Reflection across the line y = x, Reflection across the line y = -x.

Step-by-step explanation:

To determine the correct sequence of transformations that maps triangle ABC to triangle A'B'C, let's analyze the given options:

A) Rotation 180 degrees counterclockwise about the origin, Reflection across the y-axis

- This sequence involves a rotation followed by a reflection. It might not be suitable for mapping triangle ABC to A'B'C.

B) Rotation 90 degrees clockwise about the origin, Translation 4 units to the right

- This sequence includes a rotation and a translation. It may not be the correct combination for the transformation.

C) Reflection across the line x = -3, Reflection across the line y = -3

- This combination involves two reflections across vertical and horizontal lines. It doesn't seem to match the sequence needed for the transformation.

D) Reflection across the line y = x, Reflection across the line y = -x

- This option involves two reflections across diagonal lines. This sequence could be a plausible transformation.

Therefore, the correct option is:

D) Reflection across the line y = x, Reflection across the line y = -x.

This sequence of transformations is likely to map triangle ABC onto triangle A'B'C, reflecting across diagonal lines.