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 :-
Therefore, the required scale factor = k= 1.5
From the attached graph:
D = (0, 4)
F = (3, 2)
After segment DF was dilated from the origin to create segment D'F'
D' = (0, 6)
F' = (4.5, 3)
Scale factor is obtained by calculating the proportion of the coordinates of the two segments. That is ;
Scale factor = value on dilated coordinate / value on original coordinate
Taking the x-coordinate of F and F':
Scale factor = coordinate 'x' of F' / coordinate 'x' of F
Scale factor = 4.5 / 3 = 1.5
Taking the y-coordinate of F and F':
Scale factor = coordinate 'y' of F' / coordinate 'y' of F
Scale factor = 3 / 2 = 1.5