Line segment DF is dilated from the origin to create line segment D’F’ at D’ (0, 10) and F’ (7.5, 5). The original coordinates for line segment DF are D (0, 4) and F (3, 2). What scale factor was line segment DF dilated by? A: 0.5 B: 0.75 C: 1.5 D: 2.5

Answer: D. 2.5Step-by-step explanation:Given : Line segment DF is dilated from the origin to create line segment D’F’ at D' (0, 10) and F' (7.5, 5). The original coordinates for line segment DF are D(0, 4) and F(3, 2). We know that the scale factor(k) is the ratio of the coordinates of the image points and the original points.Then, [tex]k=\dfrac{\text{ y-coordinate of D'}}{\text{y-coordinate of D}}\\\\=\dfrac{10}{4}=\dfrac{5}{2}=2.5[/tex]Hence, the scale factor was line segment DF dilated by = 2.5