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?

1.5

Step-by-step explanation:

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

Similarly,

Taking the y-coordinate of F and F':

Scale factor = coordinate 'y' of F' / coordinate 'y' of F

Scale factor = 3 / 2 = 1.5

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.