Question

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. answers: A) (4, –2), (6, 8) B) (–2, 4), (6, 8) C) (–2, 4), (8, 6) D) (2, 4), (6, 8)

Answer 1

3/2

Explanation:

Answer 2

B. The endpoint of the dilated line is (-2,4),(6,8)

Explanation:

Given

Line segment AB

Endpoints: A(-3,6) and B(9,12)

Scale Factor: 2/3 about the origin

Required

Find the end points of the dilated line

From the question, we understand that the line segment is dilated about the origin;

The keywords about the origin implies that, to get the endpoints of the dilated line, we simply multiply the coordinates of of the original line by the scale factor;

This is shown below;

`For\ A = (-3,6);`

The new endpoints become

`A' = (2)/(3) A`

`A' = (2)/(3) (-3,6)`

`A' = ((2)/(3) * -3, (2)/(3) * 6)`

`A' = ((2* -3)/(3), (2 * 6)/(3))`

`A' = ((-6)/(3), (12)/(3))`

`A' = (-2, 4)`

`For\ B = (9, 12);`

The new endpoints become

`B' = (2)/(3) B`

`B' = (2)/(3) (9, 12)`

`B' = ((2)/(3) * 9, (2)/(3) * 12)`

`B' = ((2* 9)/(3), (2 * 12)/(3))`

`B' = ((18)/(3), (24)/(3))`

`B' = (6, 8)`

Hence, the endpoint of the dilated line is (-2,4),(6,8)