Question

ma.8.u7 test25-26

1. nelson is leaning a 22.5 ft

placed 13 f
a.8.u7 test25-26

1. 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?
a. each side length of quadrilateral pqrs is $\frac{1}{2}$ the corresponding side length of quadrilateral pqrs.
b. quadrilateral pqrs is similar to quadrilateral pqrs.
c. each angle measure of quadrilateral pqrs is $\frac{1}{2}$ the corresponding angle measure of quadrilateral pqrs.
d. quadrilateral pqrs is congruent to quadrilateral pqrs.

Explanation:

Dilation is a transformation that scales a figure by a scale factor from a center. Similar figures have congruent corresponding angles and proportional corresponding sides.

• Option A: The smaller figure P'Q'R'S' is the dilated image, so its sides are 1/2 of PQRS, not the reverse.
• Option B: Dilation preserves shape, so the original and dilated figures are similar.
• Option C: Dilation does not change angle measures; corresponding angles are congruent.
• Option D: Congruent figures have identical size and shape, but dilation changes size, so they are not congruent.

Answer:

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