Question

In a coordinate plane with points at A(0, 2) and B(2, 0) intersected by line F, dilate line F by a scale factor of 3 with the center of dilation at the origin to create line F′. Where are points A′ and B′ located after dilation, and how are lines F and F′ related?

a. A′ (0, 6) and B′ (6, 0); lines F and F′ are parallel.
b. A′ (0, 2) and B′ (2, 0); lines F and F′ are the same line.
c. A′ (0, 2) and B′ (6, 0); lines F and F′ intersect at point A.
d. A′ (0, 6) and B′ (2, 0); lines F and F′ intersect at point B.

Answer 1

Points A' and B' are located at A' (0, 6) and B' (6, 0) after the dilation, and lines F and F' are parallel.

Step-by-step explanation:

To dilate line F by a scale factor of 3 with the center of dilation at the origin, we need to multiply the coordinates of each point on line F by the scale factor.

Let's find the coordinates of A' and B' after dilation, using the formula (x', y') = (k * x, k * y) where (x, y) are the coordinates of the original point and k is the scale factor.

For point A (0, 2), after dilation, A' will be (0 * 3, 2 * 3) = (0, 6).

For point B (2, 0), after dilation, B' will be (2 * 3, 0 * 3) = (6, 0).

Therefore, points A' and B' are located at A' (0, 6) and B' (6, 0) after dilation.

Since the original line F goes through points A and B, and the dilated line F' goes through points A' and B', we can say that lines F and F' are parallel.