Question

Dilate line f by a scale factor of 2 with the center of dilation at the origin to create line f'. In the coordinate plane with points A(0,2) and B(2,0) intersected by line f, where are points A' and B' located after dilation, and how are lines f and f' related?

1) The locations of A' and B' are A'(0,4) and B'(4,0); lines f and f' are parallel.
2) The locations of A' and B' are A'(0,2) and B'(2,0); lines f and f' are the same line.
3) The locations of A' and B' are A'(0,2) and B'(4,0); lines f and f' intersect at point A.
4) The locations of A' and B' are A'(0,4) and B'(2,0); lines f and f' intersect at point B.

Answer 1

After dilating line f by a scale factor of 2 with the center of dilation at the origin, points A' and B' are located at (0,4) and (4,0) respectively. Lines f and f' are parallel.

Step-by-step explanation:

When a line is dilated by a scale factor of 2 with the center of dilation at the origin, each point on the original line is multiplied by 2 to determine the corresponding point on the dilated line.

In this case, for point A(0,2), the x-coordinate remains the same and the y-coordinate is multiplied by 2 to give point A'(0,4). Similarly, for point B(2,0), the y-coordinate remains the same and the x-coordinate is multiplied by 2 to give point B'(4,0).

Since the corresponding points on the dilated line f' are collinear and each point is multiplied by the same scale factor of 2, lines f and f' are parallel.