Let's use the given graph to read the coordinates of the original figure and the image of its dilation.
We can see that △ JRS and △ JKL share ∠ J, and we know that ∠ J ≅ ∠ J. Let's use the coordinates of the vertices to find the lengths of the sides of each triangle that include ∠ J.
Side
Vertices
Distance Formula
Simplified
JK
( 0,0), ( - 6,2)
sqrt(( - 6- 0)^2+( 2- 0)^2)
2 * sqrt(10)
JR
( 0,0), (- 3,1)
sqrt((- 3- 0)^2+(1- 0)^2)
sqrt(10)
JL
( 0,0), ( - 2,6)
sqrt(( - 2- 0)^2+( 6- 0)^2)
2 * sqrt(10)
JS
( 0,0), ( - 1,3)
sqrt(( - 1- 0)^2+( 3- 0)^2)
sqrt(10)
Now, we can find the ratios between the corresponding sides.
JR/JK=sqrt(10)/2 * sqrt(10) = 1/2 [1.2em]
JS/JL=sqrt(10)/2 * sqrt(10) = 1/2
We can tell that these ratios are equivalent. Therefore, the lengths of two sides of △ JRS are proportional to the lengths of two corresponding sides of △ JKL, and the included angles are congruent. By the Side-Angle-Side Similarity Theorem, we can conclude that △ JRS is similar to △ JKL.
△ JRS ~ △ JKL
Therefore, the dilation is a similarity transformation.
