Let's use the given coordinates to draw the original figure and the image of the dilation.
Let's use the coordinates of the vertices to find the lengths of the sides of each triangle.
Side
Vertices
Distance Formula
Simplified
MP
( 1,4), (2,2)
sqrt((2- 1)^2+(2- 4)^2)
sqrt(5)
ST
( - 3,6), (0,0)
sqrt(( -( - 3))^2+( - 6)^2)
3sqrt(5)
PQ
(2,2), ( 5,5)
sqrt(( 5-2)^2+( 5-2)^2)
sqrt(18)
TU
(0,0), ( 9,9)
sqrt(( 9- )^2+( 9- )^2)
3sqrt(18)
QM
( 5,5), ( 1,4)
sqrt(( 1- 5)^2+( 4- 5)^2)
sqrt(17)
US
( 9,9), ( - 3,6)
sqrt(( - 3- 9)^2+( 6- 9)^2)
3sqrt(17)
Now, we can find the ratios between the corresponding sides.
ST/MP=3sqrt(5)/sqrt(5) = 3 [1.2em]
TU/PQ=3sqrt(18)/sqrt(18) = 3 [1.2em]
US/QM=3sqrt(17)/sqrt(17) = 3
We can tell that these ratios are equivalent. Therefore, the corresponding side lengths of â–³ STU and â–³ MPQ are proportional. By the Side-Side-Side Similarity Theorem, we can conclude that â–³ STU is similar to â–³ MPQ.
â–³ STU ~ â–³ MPQ
Therefore, the dilation is a similarity transformation.
