Answer:
- A'(0,1), B'(1,0) and the lines are parallel
- dilation factor is 2
- A(-2,0), B(2,0); twice the length
Step-by-step explanation:
1. Whenever dilation is about the origin, the dilation factor affects each coordinate individually. When the dilation factor is 1/2, each coordinate of the image is 1/2 the coordinate of the pre-image:
A(0, 2) ⇒ A'(0, 1)
B(2, 0) ⇒ B'(1, 0)
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2. The above description works in reverse, as well. If the dilation factor is 1/2, the pre-image has coordinate values twice those of the image. Dilation does not change directions or angles, so any dilated lines are parallel.
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3. The center of dilation is an invariant point: it does not move. As in the second problem, the pre-image is twice the size of the image when the scale factor is 1/2.
