Answer:
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:
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)