Question

all side lengths in quadrilateral pqrs measure 4 units. a transformation maps pqrs to pqrs. all sides of pqrs measure 1 unit. is the transformation an isometric transformation? explain. yes, the side lengths in the two figures are proportional. yes, one figure maps to the other. no, the side lengths are not preserved. no, the angles are not preserved.

Explanation:

An isometric transformation preserves distances (side - lengths). Here, the side - lengths of quadrilateral \(PQRS\) are \(4\) units and the side - lengths of \(P'Q'R'S'\) are \(1\) unit. Since the side - lengths are not the same (not preserved), it is not an isometric transformation. Proportional side - lengths are not sufficient for an isometric transformation (which requires exact length preservation), and just mapping one figure to another without length preservation is not enough. There is no information given about angles, but the key factor for non - isometric here is side - length non - preservation.

Answer:

No, the side lengths are not preserved.