Question

Segment B prime C prime has endpoints located at B′(2, 0) and C′(2, 6). segment BC was dilated at a scale factor of 2 from the origin. Which statement describes the pre-image?

A. segment BC is located at B (1, 0) and C (1, 3) and is one-half the size of segment B prime C prime.
B. segment BC is located at B (2, 0) and C (2, 6) and is the same size as segment B prime C prime.
C. segment BC is located at B (4, 0) and C (4, 12) and is twice the size of segment B prime C prime.
D. segment BC is located at B (6, 0) and C (6, 18) and is three times the size of segment B prime C prime.

Answer 1

the correct statement is: BC is located at B (1, 0) and C (1, 3) and is one-half the size of B'C.

Explanation:

First, we know that B'C' was dilated at a scale factor of 2 from the origin. This means that the coordinates of the pre-image (BC) will be half of the coordinates of B'C'. Now let's find the coordinates of B and C: B = (1/2) * B' = (1/2) * (2, 0) = (1, 0) C = (1/2) * C' = (1/2) * (2, 6) = (1, 3) So, BC is located at B (1, 0) and C (1, 3). Since the scale factor was 2, BC is one-half the size of B'C'.

Answer

Therefore, the correct statement is: BC is located at B (1, 0) and C (1, 3) and is one-half the size of B'C.