Question

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. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.B. The locations of A′ and B′ are A′ (0, 2) and B′ (6, 0); lines f and f′ intersect at point A.C. The locations of A′ and B′ are A′ (0, 6) and B′ (6, 0); lines f and f′ are parallel.D. The locations of A′ and B′ are A′ (0, 6) and B′ (2, 0); lines f and f′ intersect at point B.

Answer 1

Answer: C

Explanation:

The first step is to determine the coordinates of points A and b on line F. They are

A(0, 2)

B(2, 0)

Recall, if a coordinate, (x, y) is dilated by a scale factor of b, the new coordinates would be

(bx, by)

By dilating A(0, 2), B(2, 0), the new coordinates would be

A'(0 * 3, 2 * 3) = A'(0, 6)

B'(2 * 3, 0 * 3) = B'(6, 0)

f' and f would be parallel

Thus, the correct option is

C. The locations of A′ and B′ are A′ (0, 6) and B′ (6, 0); lines f and f′ are parallel.