Let's use the given coordinates to draw the original figure and the image of its dilation.
We can see that △ VYZ and △ VWX share ∠ V, and we know that ∠ V ≅ ∠ V.
Let's use the coordinates of the vertices to find the lengths of the sides of each triangle that include ∠ V.
Side
Vertices
Distance Formula
Simplified
VX
( -3,4) and ( 1,2)
sqrt(( 1-( -3))^2+( 2- 4)^2)
2sqrt(5)
VZ
( -3,4) and (3,1)
sqrt((3-( -3))^2+(1- 4)^2)
3sqrt(5)
VW
( -3,4) and ( -5,0)
sqrt(( -5-( -3))^2+( 0- 4)^2)
2sqrt(5)
VY
( -3,4) and ( -6,-2)
sqrt(( -6-( -3))^2+( -2- 4)^2)
3sqrt(5)
Now, we can find the ratios between the corresponding sides.
VZ/VX=3sqrt(5)/2sqrt(5) = 3/2 [1.2em]
VY/VW=3sqrt(5)/2sqrt(5) = 3/2
We can tell that these ratios are equivalent. Therefore, the lengths of two sides of △ VYZ are proportional to the lengths of two corresponding sides of △ VWX, and the included angles are congruent. By the Side-Angle-Side Similarity Theorem, we can conclude that △ VYZ is similar to △ VWX.
△ VYZ ~ △ VWX
Therefore, the dilation is a similarity transformation.
