Question

1) Dilate line f by a scale factor of 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?

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

Answer 1

In geometry, dilating line f with a scale factor of 2, points A and B on line f are relocated to A' (0, 2) and B' (2, 0) respectively. Consequently, lines f and f' become the same line and are overlapping, meaning they are parallel to each other.

Step-by-step explanation:

The question appears to relate to mathematics, specifically to the topic of dilation in geometry. Dilation involves resizing a shape by a certain scale factor with respect to a center of dilation, which in this case is specified to be the origin (0,0). When a line is dilated by a scale factor with respect to the origin, each point on the line is moved radially away from or towards the origin by that scale factor.

If we assume that line f passes through points A (0, 1) and B (1, 0), dilating this line with a scale factor of 2 and the origin as the center of dilation will double the distance of each point from the origin. Therefore, the new points after dilation will be A' (0, 2) and B' (2, 0). This means that line f will not change its direction, making lines f and f' the same. Thus, they will be parallel lines overlapping each other (coinciding).