Question

CD was dilated around the origin by a scale factor of 2. The endpoints of the image are C'(4,0) and D'(6,2). What are the coordinates of the endpoints of the original line segment?

A) C(2,0), D(3,0).
B) C(2,0), D(3,1).
C) C(2,0), D(1,1).
D) C(4,0), D(6,2).

Answer 1

The endpoints of the original line segment CD are C(2,0) and D(3,1) after dividing the coordinates of the dilated segment C'D' by the scale factor of 2.

Step-by-step explanation:

If CD was dilated around the origin by a scale factor of 2 and the endpoints of the image are C'(4,0) and D'(6,2), we can find the coordinates of the endpoints of the original line segment CD by dividing each of the coordinates of C' and D' by the scale factor.

For C'(4,0), we divide both coordinates by 2:
C(4 ÷ 2, 0 ÷ 2) = C(2, 0)

Similarly, for D'(6,2), we divide both coordinates by 2:
D(6 ÷ 2, 2 ÷ 2) = D(3, 1)

Therefore, the coordinates of the original endpoints of line segment CD are C(2,0) and D(3,1), which corresponds to option B.