Question

Segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3). segment YZ was dilated at a scale factor of 3 from the origin. Which statement describes the pre-image?
A. segment YZ is located at Y (0, 9) and Z (−18, 9) and is three times the size of segment Y prime Z prime.
B. segment YZ is located at Y (0, 3) and Z (−6, 3) and is the same size as segment Y prime Z prime.
C. segment YZ is located at Y (0, 1.5) and Z (−3, 1.5) and is the one-half the size of segment Y prime Z prime.
D. segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime.

Answer 1

Answer:

D. Segment YZ is located at Y(0,1) and Z(−2,1) and is one-third the size of segment Y'Z'

Step-by-step explanation:

When you dilate a point by a factor of x from the origin, you multiply its coordinates by the same factor.

Thus, if the coordinates of the original point are (1,2) and the scale factor is 3, those of its image are (3,6).

If Y'Z' has endpoints at Y'(0,3) and Z'(-6,3) and was dilated by a factor of 3, the coordinates of the endpoints of the pre-image were ⅓ those of the image.

The figure below shows the segments YZ and Y'Z'.