the trapezoid pqrs is a dilation of the trapezoid pqrs. what is the scale factor of the dilation? simplify…

the trapezoid pqrs is a dilation of the trapezoid pqrs. 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.

the trapezoid pqrs is a dilation of the trapezoid pqrs. 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.

Answer

Explanation:

Step1: Select a corresponding side

Let's consider side $PS$ and $P'S'$. The length of $PS$ can be found by calculating the difference in $x -$coordinates of $P(8,8)$ and $S(-8,8)$. So $PS=\vert8 - (-8)\vert=16$. The length of $P'S'$ can be found by calculating the difference in $x -$coordinates of $P'(6,6)$ and $S'(-6,6)$. So $P'S'=\vert6-(-6)\vert = 12$.

Step2: Calculate the scale - factor

The scale factor $k$ of a dilation is given by the ratio of the length of the corresponding side of the image to the length of the corresponding side of the pre - image. So $k=\frac{P'S'}{PS}$. Substituting the values we found: $k = \frac{12}{16}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$