Point F(x, y) = (- 3, - 1) is a dilation of the black point with a scale factor of 3.
What is the location of the image of a given point on Cartesian plane?
In this problem we must determine the coordinates of the image of a black point, which is the result of a dilation with a scale factor of 3. Please notice that both center of dilation, the black point and the image (a blue point) are colinear. The procedure is now shown:
First, determine the coordinates of the expected image:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
- O(x, y) - Coordinates of the center of dilation.
- P(x, y) - Coordinates of the black point.
- k - Scale factor.
(O(x, y) = (- 6, 5), k = 3, P(x, y) = (- 5, 3))
P'(x, y) = (- 6, 5) + 3 · [(- 5, 3) - (- 6, 5)]
P'(x, y) = (- 6, 5) + 3 · (1, - 2)
P'(x, y) = (- 6, 5) + (3, - 6)
P'(x, y) = (- 3, - 1)
Second, check what point matches with result found in the previous step:
P'(x, y) = F(x, y)