Question

quadrilateral pqrs is dilated with the origin as the center of dilation to create quadrilateral pqrs. the coordinates of each vertex are integers. which statement is true? each side length of quadrilateral pqrs is 1/2 the corresponding side lengths of quadrilateral pqrs. quadrilateral pqrs is congruent to quadrilateral pqrs. each angle measure of quadrilateral pqrs is 1/2 the corresponding angle measure of quadrilateral pqrs. quadrilateral pqrs is similar to quadrilateral pqrs.

Explanation:

Step1: Recall dilation properties

Dilation is a transformation that changes the size of a figure. Corresponding angles of the original figure and the dilated figure are equal. Corresponding side - lengths are proportional.

Step2: Analyze congruence and similarity

Since dilation changes the size of the figure, the two figures are not congruent. But they are similar because the shape remains the same (equal angles and proportional side - lengths). Angle measures remain the same in dilation, so angles of PQRS and P'Q'R'S' are equal, not half. Also, from the graph, we can see that the side - lengths of P'Q'R'S' are half of the side - lengths of PQRS, not the other way around as stated in the first option.

Answer:

Quadrilateral P'Q'R'S' is similar to quadrilateral PQRS.