Question

reflected over the line y = x; rotate 90° clockwise around the point (-1, 2); rotate 180° around the point (0, 0); translate right 3 and down 2 (accompanied by a coordinate grid with two triangles labeled a, b, c and a, b, c)

Explanation:

To determine the transformation, we analyze each option:

• Reflect over \( y = x \): Swaps \( x \) and \( y \)-coordinates. The orientation and position don’t match this reflection.
• Rotate \( 90^\circ \) clockwise around \( (-1, 2) \): The center \( (-1, 2) \) is not consistent with the symmetry seen (e.g., distances from a central point like \( (0,0) \) are more intuitive).
• Rotate \( 180^\circ \) around \( (0,0) \): A \( 180^\circ \) rotation around the origin maps \( (x, y) \to (-x, -y) \). For example, if \( A \) is \( (-1, 2) \), rotating \( 180^\circ \) gives \( (1, -2) \), which aligns with \( A' \)’s position. The triangle’s orientation (flipped both horizontally and vertically) matches a \( 180^\circ \) rotation about the origin.
• Translate right 3 and down 2: A translation would shift the triangle without rotating or reflecting; the orientation change (flipped) rules this out.

Answer:

Rotate \( 180^\circ \) around the point \( (0, 0) \)