Question

The line segment is dilated by a factor of 1/2 with respect to the origin. What is the length of the dilated line segment?

A. 1 unit


B. 2 units


C. 3 units


D. 4 units

Answer 1

The length of the dilated line segment is 2 units. ( option B)

A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.

Scale factor = Dimension of new length /dimension of original length

The dimension of the original length is 4 units

scale factor = 1/2

let the new length be x

Therefore;

1/2 = x/4

2x = 4

x = 4/2 = 2units

Therefore, the length of the dilated segment is 2units

Answer 2

A dilation is a transformation that produces an image that is the same shape as the original, but different size. A dilation stretches or shrinks the original figure.
In this case the scale factor is 1/2, therefore the image will be smaller than the original line.
Original line is 4 units
The dilated line segment will be 1/2 x 4 = 2 units