Question

quadrilateral nopq is dilated by a scale factor of \\(\frac{3}{4}\\) to form quadrilateral nopq. what is the measure of side qn? \
image of rectangle nopq with qp = 42, po = 21, on = 42, nq = 21

Explanation:

Step1: Recall dilation property

In a dilation, the ratio of corresponding sides of the image (dilated figure) to the original figure is equal to the scale factor. Let the length of side QN be \( x \). The length of its corresponding side \( Q'N' \) is 21, and the scale factor \( k=\frac{3}{4} \). So, \( \frac{Q'N'}{QN}=k \), which means \( \frac{21}{x}=\frac{3}{4} \).

Step2: Solve for \( x \)

Cross - multiply the equation \( \frac{21}{x}=\frac{3}{4} \). We get \( 3x = 21\times4 \). Then \( 3x=84 \). Divide both sides by 3: \( x=\frac{84}{3}=28 \).

Answer:

28