Question

the rectangle qrst is a dilation of the rectangle qrst. 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: Find side - length of original and dilated rectangles

The length of side $QT$ of rectangle $QRST$: The $x$ - coordinates of $Q(10,2)$ and $T(-8,2)$ are used. $QT=\vert10 - (-8)\vert=18$. The length of side $Q'T'$ of rectangle $Q'R'S'T'$: The $x$ - coordinates of $Q'(6,2)$ and $T'(-4,2)$ are used. $Q'T'=\vert6-(-4)\vert = 10$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. $k=\frac{Q'T'}{QT}=\frac{10}{18}=\frac{5}{9}$.

Answer:

$\frac{5}{9}$