Question

+

Select the correct answer.
AABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image AABC. If A=(2, 2), B=(4, 3), and C= (6, 3).
what is the length of B'C'?
OA
OB.
OC
OD.
3 units
4 units
2 units
1 unit

Answer 1

(d) 1 unit

Explanation:

The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.

Original line segment

The length of the original horizontal line segment BC is the difference of its x-coordinates:

BC = 6 -4 = 2 . . . . units

(We know the segment is horizontal because the y-coordinates of the end points are the same.)

Dilated segment

Multiplying the length of the original segment by the dilation factor, we find the length of B'C':

B'C' = dilation factor × BC

B'C' = 0.5×(2 units)

B'C' = 1 unit

Dilated Coordinates

The dilation factor multiplies each coordinate value:

B' = 0.5B = 0.5(4, 3) = (2, 1.5)

C' = 0.5C = 0.5(6, 3) = (3, 1.5)

The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.