Question

Question 1 (5 points)

The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale
factor 2/3 about the origin. Find the endpoints of the dilated line segment.
OA) (-2, 4), (6,8)
B) (2, 4). (6,8)
OC) (4, -2), (6,8)
OD) (-2,4), (8,6)​

Answer 1

Answer: A) (-2, 4), (6,8)

Explanation:

When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).

Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor
`\frac23` about the origin.

Let A' and B' b the endpoints of the dilated line segment.

Then,
`A'((2)/(3)(-3), \frac23(6))=A'(-2,4)`

`B'((2)/(3)(9), \frac23(12))=B'(6,8)`

Hence, the correct option is A) (-2, 4), (6,8)