Question

is pqrs similar to uvwx? justify your answer.
yes, because a translation right 1 unit and up 8 units maps pqrs onto uvwx.
yes, because a rotation 90° clockwise around the origin maps pqrs onto uvwx.
no, because ∠r and ∠w do not have the same measure.

Explanation:

Step1: Analyze translation

Translation is a rigid transformation that preserves shape and size. If PQRS is translated right 1 unit and up 8 units, the two figures PQRS and UVWX would be congruent (a special case of similarity with scale factor 1). But we need to check if the correspondence is correct.

Step2: Analyze rotation

Rotation is a rigid transformation. A \(90^{\circ}\) clock - wise rotation around the origin changes the orientation of the figure. If we assume the coordinates of the vertices of PQRS and UVWX, a \(90^{\circ}\) clock - wise rotation \((x,y)\to(y, - x)\) (for a rotation about the origin) does not map PQRS onto UVWX as the relative positions of the vertices (in terms of the grid) do not match this transformation rule.

Step3: Analyze angle - measure condition for similarity

For two polygons to be similar, their corresponding angles must be equal. If \(\angle R\) and \(\angle W\) do not have the same measure, then by the definition of similar polygons (all corresponding angles are equal and all corresponding sides are in proportion), PQRS is not similar to UVWX.

Answer:

No, because \(\angle R\) and \(\angle W\) do not have the same measure.