The table shows the ordered pairs that represent the vertices of triangle one and its image triangle to after a dilation with the origin as the center of dilation

Question

Triangle one Triangle two
X. Y. X. Y
2 -2 10 -10
3 -6 15. -30
5 -4 25. -20

Which rule best represents the dilation that was applied to triangle one to create triangle to

Answer 1

To find the rule for the dilation that was applied to triangle one to create triangle two, we can analyze how the x and y coordinates of each vertex changed.

For the first point (2, -2) in triangle one, it dilated to (10, -10) in triangle two.
The x coordinate increased by a factor of 5 (10/2 = 5) and the y coordinate increased by a factor of 5 (-10/-2 = 5).

Therefore, the rule for the dilation in this case is:

Dilation by a factor of 5: (x, y) -> (5x, 5y)