Question

be dilated with the origin as the center of dilation using the rule (x,y) → (3.75x, 3.75y).
which statement is true?

• each angle measure of quadrilateral lmpq will be 3.75 times the corresponding angle measure of quadrilateral lmpq.
• each angle measure of quadrilateral lmpq will be 3.75 more than the corresponding angle measure of quadrilateral lmpq.
• each side length of quadrilateral lmpq will be 3.75 times the corresponding side length of quadrilateral lmpq.
• each side length of quadrilateral lmpq will be 3.75 more than the corresponding side length of quadrilateral lmpq.

Explanation:

Step1: Recall Dilation Properties

Dilation is a transformation that scales a figure by a scale factor \( k \) from a center (here, origin). For dilation with rule \((x,y)\to(kx,ky)\), the scale factor is \( k \). Angles in a dilated figure are congruent (same measure) to original, and side lengths are scaled by \( k \) (multiplied, not added).

Step2: Analyze Each Option

• Option 1: Angles don’t scale (dilation preserves angle measure), so "3.75 times" is wrong.
• Option 2: Angles don’t increase by a constant (dilation preserves angles), so "3.75 more" is wrong.
• Option 3: Dilation with scale factor \( 3.75 \) means side lengths are multiplied by \( 3.75 \), which matches dilation properties.
• Option 4: Side lengths are scaled (multiplied) by \( 3.75 \), not increased by \( 3.75 \), so wrong.

Answer:

Each side length of quadrilateral \( L'M'P'Q' \) will be \( 3.75 \) times the corresponding side length of quadrilateral \( LMPQ \). (The option with this statement, e.g., the third option in the list)