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

Explanation:

Step1: Select corresponding side lengths

Let's consider the vertical side - length of the trapezoids. For trapezoid $KLMN$, the vertical distance from $K$ to $N$ (or $L$ to $M$) can be found. The $y$ - coordinate of $K$ is 10 and the $y$ - coordinate of $N$ is - 10, so the length of the vertical side of trapezoid $KLMN$ is $|10-(-10)| = 20$. For trapezoid $K'L'M'N'$, the $y$ - coordinate of $K'$ is 8 and the $y$ - coordinate of $N'$ is - 8, so the length of the vertical side of trapezoid $K'L'M'N'$ is $|8 - (-8)|=16$.

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 image to the length of the corresponding side of the pre - image. So, $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}=\frac{16}{20}$.

Step3: Simplify the fraction

Simplify $\frac{16}{20}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4. $\frac{16\div4}{20\div4}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$