Question

line segment DF on a coordinate plane with D at 0 comma 4 and F at 3 comma 2 segment DF is dilated from the origin to create segment D prime F prime at D′ (0, 6) and F′ (4.5, 3). What scale factor was segment DF dilated by? 0.75 1.3 1.5 2.5

Answer 1

Answer: 1.5

Step-by-step explanation:

We know that when a figure is dilated from the origin , then the scale factor if dilation is the ratio of the coordinate of image to the pre-image.

Given : line segment DF on a coordinate plane with D at (0,4) and F at (3,2) segment DF is dilated from the origin to create segment D prime F prime at D′ (0, 6) and F′ (4.5, 3).

Then, the scale factor will be :-

$k=\dfrac{\text{x-coordinate of D'}}{\text{\text{x-coordinate of D}}}\\\\=\dfrac{6}{4}=1.5$

Therefore, the required scale factor = k= 1.5