[email protected] wrote:
What are the coordinates for the point on Line AB (see figure) that is three times as far from A as from B, and that is in between points A and B?

The question is essentially asking us to find the coordinates of a point (call point C) such that length AC is 3 times length BC.

Consider the right triangle with AB as the hypotenuse.


Now divide the two legs into 4 parts.


If we draw a right triangle like so, we'll see that the red triangle is 1/4 the size of the original blue triangle.


IMPORTANT: This means that the distance from A to C is THREE TIMES the distance from C to B. So, point C satisfies the given information.

Now all we need to do is determine the size of the red triangle.


Since the red triangle is 1/4 the size of the blue triangle, its sides have lengths 3/4 and 1 1/2.
So, to the find the coordinates of C, just factor these lengths into the coordinates of point B.

So, the x-coordinate of point C = (-2) - (3/4) = -2 3/4 (aka -2.75)
The y-coordinate of point C = (0) + (1 1/2) = 1 1/2 (aka 1.5)

So the coordinates are [spoiler](-2.75, 1.5)[/spoiler]

Cheers,
Brent

Hi shibsriz,

In these types of questions, the answers choices usually are written in such a way that you can quickly eliminate some (or even all) of the wrong answers because those answers can't possibly be what you're looking for (in this question, they couldn't be on the line). Use all the information that you're given and you'd be amazed how many shortcuts you'll find on Test Day.

GMAT assassins aren't born, they're made,
Rich