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.

O A) (2, 4), (6,8)

B) (4, -2), (6,8)

O C) (-2, 4), (6,8)

OD) (-2, 4), (8,6)

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale  factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

Here,

Putting all the values and finding AB:

It is given that AB is dilated with a scale factor of .

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

So, option C) (-2, 4), (6,8) is the correct answer.

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