Question

the triangle klm is a dilation of the triangle klm. 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: Select a pair of corresponding sides

Let's consider side $KL$ and $K'L'$.

Step2: Find the lengths of corresponding sides

The length of $KL$: Using the distance - formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, for $K(3,3)$ and $L(6,3)$, $KL=\vert6 - 3\vert=3$. For $K'(4,4)$ and $L'(8,4)$, $K'L'=\vert8 - 4\vert = 4$.

Step3: 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. So $k=\frac{K'L'}{KL}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$