Question

For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation. Then graph the preimage and image on a separate sheet of paper.

D(2,−2), E(4, −2), F(1, −4), k=1.5,
centered at E

Answer 1

The images of the triangle vertices are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).

How to determine the images of triangle vertices by rigid transformations

In this problem we find the three vertices of a triangles, whose image is the result of a rigid transformation known as dilation. The dilation formula is defined below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

• O(x, y) - Origin
• k - Dilation scale.
• P(x, y) - Original point.
• P'(x, y) - Image

If we know that O(x, y) = (4, - 2), D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices are, respectively:

D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]

D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)

D'(x, y) = (4, - 2) + (- 3, 0)

D'(x, y) = (1, - 2)

E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]

E'(x, y) = (4, - 2)

F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]

F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)

F'(x, y) = (4, - 2) + (- 4.5, - 3)

F'(x, y) = (- 0.5, - 5)