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?

segment BC is located at B (1, 0) and C (1, 3) and is one-half the size of segment B prime C prime.
segment BC is located at B (2, 0) and C (2, 6) and is the same size as segment B prime C prime.
segment BC is located at B (4, 0) and C (4, 12) and is twice the size of segment B prime C prime.
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 pre-image segment BC, after a dilation with a scale factor of 2 from the origin, is located at B (1, 0) and C (1, 3) and is half the size of segment B'C'.

Step-by-step explanation:

In the given problem, you have mentioned that segment B'C' has endpoints at B′(2, 0) and C′(2, 6), and that segment BC has been subjected to a dilation with a scale factor of 2 from the origin. This means that the distances from the origin of every point of segment BC to the corresponding point of segment B'C' are twice as large.

Therefore, to find the coordinates of the endpoints of segment BC, we must halve the coordinates of the endpoints of segment B'C'. The coordinates of B' are (2,0), so the coordinates of B must be (2/2, 0/2), which simplifies to (1, 0). Similarly, the coordinates of C' are (2, 6), so the coordinates of C must be (2/2, 6/2), simplifying to (1, 3).

Thus, the pre-image segment BC is located at B (1, 0) and C (1, 3) and is one-half the size of segment B'C', describing the first statement as correct. A dilation with a scale factor less than 1 reduces the size of the object, hence the relationship between BC and B'C'.