Let's use the given graph to read the coordinates of the original figure and the image of its dilation.
We can see that △ ABC and △ ADE share ∠ A, and we know that ∠ A ≅ ∠ A. Let's use the coordinates of the vertices to find the lengths of the sides of each triangle that include ∠ A.
Side
Vertices
Distance Formula
Simplified
AD
( 0,0), ( - 2,- 2)
sqrt(( - 2- 0)^2+( - 2- 0)^2)
2 * sqrt(2)
AB
( 0,0), (- 4,- 4)
sqrt((- 4- 0)^2+(- 4- 0)^2)
4 * sqrt(2)
AE
( 0,0), ( 2,- 1)
sqrt(( 2- 0)^2+( - 1- 0)^2)
sqrt(5)
AC
( 0,0), ( 4,- 2)
sqrt(( 4- 0)^2+( - 2- 0)^2)
2 * sqrt(5)
Now, we can find the ratios between the corresponding sides.
AB/AD=4 * sqrt(2)/2 * sqrt(2) =2 [1.2em]
AC/AE=2 * sqrt(5)/sqrt(5) =2
We can tell that these ratios are equivalent. Therefore, the lengths of two sides of △ ABC are proportional to the lengths of two corresponding sides of △ ADE, and the included angles are congruent. By the Side-Angle-Side Similarity Theorem, we can conclude that △ ABC is similar to △ ADE.
△ ABC ~ △ ADE
Therefore, the dilation is a similarity transformation.
