Question

in the figure shown, which composition of rigid transformations will map one triangle onto the other? a. a glide reflection b. a reflection followed by a translation c. two translations d. a rotation followed by a translation

Explanation:

Step1: Analyze Rigid Transformations

Rigid transformations (reflection, rotation, translation) preserve shape and size. Let's analyze each option:

• Option A (Glide Reflection): A glide reflection is a reflection followed by a translation. But first, check if a glide reflection applies. The triangles have a rotated orientation (angle position changed), so a glide reflection (which is reflection + translation) doesn't match the rotation - like change.
• Option B (Reflection + Translation): A reflection would flip the triangle, but the key is the angle's position. The top triangle's angle is at the top, the bottom one's angle is at the right. A reflection followed by translation doesn't account for the rotational change.
• Option C (Two Translations): Translations only move the figure without rotating or reflecting. The triangles have a rotational difference (angle position), so two translations can't map them.
• Option D (Rotation + Translation): First, rotate the top triangle to align the angle (and sides) with the bottom triangle's orientation, then translate to move it to the correct position. This matches the visual: the angle's position and side markings suggest a rotation (to align the angle) followed by a translation (to move it down/over).

Answer:

D. a rotation followed by a translation