Question

the rectangle nopq is a dilation of the rectangle nopq. what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding side lengths

Length of $OP$: distance between $(-8,6)$ and $(9,6)$ is $17$. Length of $O'P'$: distance between $(-4,3)$ and $(5,3)$ is $9$. Correction: Use horizontal side NQ and N'Q'
Length of $NQ$: from $(-8,-2)$ to $(9,-2)$ is $17$. Length of $N'Q'$: from $(-4,-2)$ to $(5,-2)$ is $9$. Better: Use horizontal segment from x-coordinates: For original, $P$ is at $x=9$, $O$ at $x=-8$, so length $9 - (-8) = 17$. For image, $P'$ at $x=5$, $O'$ at $x=-4$, so length $5 - (-4) = 9$. Alternatively, use vertical side: $O$ at $y=6$, $N$ at $y=-2$, length $6 - (-2)=8$. $O'$ at $y=3$, $N'$ at $y=-2$, length $3 - (-2)=5$. Wait, vertical length original: $8$, image: $5$. Scale factor is $\frac{\text{image length}}{\text{original length}}$

Step2: Calculate scale factor

Scale factor = $\frac{\text{Length of image side}}{\text{Length of original side}}$ = $\frac{5}{8}$ (using vertical sides: $O'N' = 5$, $ON=8$)

Answer:

$\frac{5}{8}$