The problem states that triangle $J'K'L'$ is a dilation of triangle $JKL$. We need to find the scale factor of the dilation.

1. Problem Description

The problem states that triangle $J'K'L'$ is a dilation of triangle $JKL$. We need to find the scale factor of the dilation.

2. Solution Steps

The scale factor of a dilation can be found by dividing the length of a side in the image by the length of the corresponding side in the pre-image. We can find the coordinates of the vertices of the triangles from the graph.

$J = (-3, 4)$

$K = (-3, -4)$

$L = (1, -4)$

$J' = (-6, 8)$

$K' = (-6, -8)$

$L' = (2, -8)$

Let's find the length of side $JK$ and side $J'K'$.

The length of $JK$ is $4 - (-4) = 8$.

The length of $J'K'$ is $8 - (-8) = 16$.

The scale factor is the ratio of the lengths of the corresponding sides:

$k = \frac{J'K'}{JK} = \frac{16}{8} = 2$

Alternatively, we could find the distance from the origin to each point. If we assume the center of dilation is at the origin (0,0), we can check the scale factor by comparing coordinates.

$J = (-3, 4)$, $J' = (-6, 8)$. Since $-3*2 = -6$ and $4*2 = 8$, the scale factor is

2. $K = (-3, -4)$, $K' = (-6, -8)$. Since $-3*2 = -6$ and $-4*2 = -8$, the scale factor is

2. $L = (1, -4)$, $L' = (2, -8)$. Since $1*2 = 2$ and $-4*2 = -8$, the scale factor is

2.

3. Final Answer

The scale factor of the dilation is 2.