Exercise 17 Page 515

Let's use the given coordinates to draw the original figure and the image of its dilation.

Let's use the coordinates of the vertices to find the lengths of the sides of each triangle.

Side	Vertices	Distance Formula	Simplified
$\overline{JK}$	$(\text{-}6,8),$ $(6,6)$	$\sqrt{(6-(\text{-}6){)}^2+(6-8{)}^2}$	$2\sqrt{37}$
$\overline{DG}$	$(\text{-}12,16),$ $(12,12)$	$\sqrt{(12-(\text{-}12){)}^2+(12-16{)}^2}$	$4\sqrt{37}$
$\overline{KL}$	$(6,6),$ $(\text{-}2,4)$	$\sqrt{(\text{-}2-6{)}^2+(4-6{)}^2}$	$2\sqrt{17}$
$\overline{GH}$	$(12,12),$ $(\text{-}4,8)$	$\sqrt{(\text{-}4-12{)}^2+(8-12{)}^2}$	$4\sqrt{17}$
$\overline{LJ}$	$(\text{-}2,4),$ $(\text{-}6,8)$	$\sqrt{(\text{-}6-(\text{-}2){)}^2+(8-4{)}^2}$	$4\sqrt{2}$
$\overline{HD}$	$(\text{-}4,8),$ $(\text{-}12,16)$	$\sqrt{(\text{-}12-(\text{-}4){)}^2+(16-8{)}^2}$	$8\sqrt{2}$

Now, we can find the ratios between the corresponding sides. We can tell that these ratios are equivalent. Therefore, the corresponding side lengths of $△JKL$ and $△DGH$ are proportional. By the Side-Side-Side Similarity Theorem, we can conclude that $△JKL$ is similar to $△DGH.$ Therefore, the dilation is a similarity transformation.