Question

Geometry Dilation

Please help!!!!

Answer 1

C' (-2, -2)

D' (-2, 2)

E' (2, 0)

F' (0, -2)

Explanation:

A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.

It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.

Therefore, the rule for a dilation of 2 about the origin is:

• (x, y) → (2x, 2y)

From inspection of the given diagram, the vertices of the pre-image are:

• C = (-1, -1)
• D = (-1, 1)
• E = (1, 0)
• F = (0, -1)

Applying the dilation rule (x, y) → (2x, 2y):

• C' = (2 · -1, 2 · -1) = (-2, -2)
• D' = (2 · -1, 2 · 1) = (-2, 2)
• E' = (2 · 1, 2 · 0) = (2, 0)
• F' = (2 · 0, 2 · -1) = (0, -2)