Question

△qrs is the image of △qrs after a reflection across the y - axis and a translation 3 units down. is the image the same size and shape as the preimage? △qrs and △qrs, the same size and shape.

Explanation:

Step1: Recall Transformations Properties

Reflections and translations are rigid transformations. Rigid transformations (like reflection, translation, rotation) preserve the size and shape of a figure, meaning the image and preimage are congruent (same size and shape).

Step2: Analyze the Given Transformations

The triangle \( \triangle QRS \) undergoes a reflection over the \( y \)-axis (a rigid transformation) and then a translation 3 units down (also a rigid transformation). Since both transformations are rigid, the image \( \triangle Q'R'S' \) should have the same size and shape as the preimage \( \triangle QRS \).

Answer:

Yes, the image \( \triangle Q'R'S' \) is the same size and shape as the preimage \( \triangle QRS \) because reflection and translation are rigid transformations that preserve the figure's size and shape.