Question

select one select one 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

Explanation:

To determine the transformation, we analyze each option:

• Reflect over \( y = x \): Swaps \( x \) and \( y \) coordinates. The triangles don't show this swap.
• Rotate \( 90^\circ \) clockwise around \( (-1, 2) \): The orientation and position don't match a \( 90^\circ \) rotation around that point.
• Rotate \( 180^\circ \) around \( (0, 0) \): A \( 180^\circ \) rotation around the origin changes \( (x, y) \) to \( (-x, -y) \). Observing the points, this transformation aligns the triangles (e.g., if \( A \) is \( (-1, 2) \), rotating \( 180^\circ \) around \( (0,0) \) gives \( (1, -2) \), which matches \( A' \)’s position).
• Translate right 3 and down 2: The movement doesn't match the relative position of the triangles.

Answer:

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