Question

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

Explanation:

Step1: Select corresponding side lengths

Let's consider the vertical side - length of the rectangles. The length of the vertical side of rectangle $KLMN$ from $L$ to $K$ is $6$ (from $y = 0$ to $y = 6$). The length of the vertical side of rectangle $K'L'M'N'$ from $L'$ to $K'$ is $2$ (from $y = 0$ to $y = 2$).

Step2: Calculate the scale - factor formula

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. So, $k=\frac{\text{length of side in dilated figure}}{\text{length of corresponding side in original figure}}$.

Step3: Substitute the values

Substituting the values of the side - lengths we found, we have $k=\frac{2}{6}$.

Step4: Simplify the fraction

Simplifying $\frac{2}{6}$ by dividing both the numerator and the denominator by their greatest common divisor (which is 2), we get $k = \frac{1}{3}$.

Answer:

$\frac{1}{3}$