Question

Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin. (1 point) The scale factor is _
AB= (-3,4) (2,-4)
AB= (-6,8) (4,-8)

Answer 1

To find the scale factor, we can compare the distances between the corresponding points of the original and dilated lines.

The distance between the points (-3,4) and (-6,8) in the original line AB is calculated as follows:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(-6 - (-3))^2 + (8 - 4)^2]
Distance = √[(-3)^2 + 4^2]
Distance = √[9 + 16]
Distance = √25
Distance = 5

Now, let's calculate the distance between the corresponding points (2,-4) and (4,-8) in the dilated line AB:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(4 - 2)^2 + (-8 - (-4))^2]
Distance = √[2^2 + (-4)^2]
Distance = √[4 + 16]
Distance = √20
Distance = 2√5

To find the scale factor, we divide the distance of the dilated line by the distance of the original line:

Scale factor = Distance of Dilated Line / Distance of Original Line
Scale factor = (2√5) / 5
Scale factor = √5 / 5

Therefore, the scale factor used in the dilation of line AB is √5 / 5.