Transformations

Question

Triangles GEO and ALG are similar with points G(-2,6) E(1,7) O(4,4) - A(-10,0) L(-1,3) G(8,-6)

Triangle ALG is the image of triangle GEO.

Find the center of dilation and the scale factor.

Answer 1

Draw straight lines in the coordinate plane through each of the 3 corresponding vertices. Where the lines intersect is the center of dilation.

Determine the equations of the three lines using the two points:

Through G and A it is y = (3/4)x + 15/2

Through E and L it is y = 2x + 5

Through O and G it is (-5/2)x + 14

In the coordinate plane they will intersect at (2,9)

To figure the scale factor, determine horizontal and vertical distance you need to go from the center of dilation (2,9) to point E (1,7) which is to the left 1 and down 2.

Do the same to see what you need to go from (2,9) to corresponding vertices L (-1,3). To the left 3 and down 6.

The horizontal and vertical distance travelled is 3 times to go to point L than it is to go to point E, so the scale factor is 3.