Question

Coordinate plane with segment AB located at A (0, 2) and B (2, 3). Segment AB is dilated from the origin to create segment A'B' at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?

Select one:
a. One-half
b. 2
c. 3
d. 4

Answer 1

The scale factor for the dilation of segment AB to segment A'B' is 2, as each coordinate has been doubled from the original segment to the dilated segment.

Step-by-step explanation:

The dilation of segment AB to segment A'B' is a transformation that increases the size of the segment by a certain scale factor. To find the scale factor, we can compare the coordinates of A with A' and B with B'. The y-coordinate of A was originally 2 and has increased to 4 in A', which is a multiplication by 2. Similarly, the x-coordinate of B went from 2 to 4, also multiplied by 2, and the y-coordinate went from 3 to 6, which again is a multiplication by 2. Thus, the scale factor of the dilation is 2, as every coordinate of the original segment AB has been multiplied by 2 to get segment A'B'.