Question

BC has endpoints located at B (2.0) and C(2,6). BC was dilated at a scale factor of 2 from the origin. Which statement describes the pre-image?

Options:
A, BC is located at B (1.0) and C (1.3) and is one-half the size of BC.
B. BC is located at B (2.0) and C (2.6) and is the same size as BC.
C. BC is located at B (4.0) and C (4.12) and is twice the size of BC.
D. BC is located at B (6.0) and C (6.18) and is three times the size of BC.

Answer 1

The correct statement after dilating segment BC with endpoints B (2,0) and C (2,6) by a scale factor of 2 from the origin is that the segment's endpoints become B (4.0) and C (4,12), and it is twice the size of the original.

Step-by-step explanation:

The question involves understanding the concept of dilation in geometry. When a figure is dilated by a scale factor from the origin, the distances of its points from the origin are multiplied by that scale factor. Given the endpoints B (2,0) and C (2,6), if we apply a scale factor of 2, the points will be at new coordinates B' (4,0) and C' (4,12). The new segment B'C' will be twice the length of the original segment BC, because each coordinate is multiplied by the scale factor of 2. Therefore, the correct option is C, which states that BC is located at B (4.0) and C (4,12) and is twice the size of BC.