REALLY NEED HELP

Can you be more specific? There isn't one "golden rule" which can be applied for various figures.

Co-ordinate points are just another way to get the length of the various sides of the figure.

During a practice test I was given a problem that invovled two triangles. They gave the coordinate pairs for the different letters of each corresponding triangle and asked what fraction was the area of one triangle to the other. I would like to know how go solving such a question.

Good question - keep in mind that, however tricky it may seem, coordinate geometry is a perfect GMAT discipline in that you always have more information than meets the eye. How?

Coordinate geometry is conducted on the coordinate plane - a grid chock full of right angles!

Geometry on the GMAT tends to more often than not center on your ability to find right angles so that you can employ what you know about squares, rectangles, and most importantly right triangles. So, when you're faced with anything on the coordinate plane, know that you're not far away from being able to create right angles so that you can take advantage of them.

Say you were given two points: (3, 3) and (7, 6). The x and y axes will always intersect at right angles, so you can take the horizontal distance (the difference in x: 7-3 = 4) and the vertical distance (the difference in y: 6-3 = 3) and create a triangle with each of those distances forming the two shorter legs of a right triangle. With legs of 3 and 4, the right triangle would have a third side of 5 (using the 3-4-5 ratio, or 3^2 + 4^2 = c^2 to solve), and you have your distance between those points.

Using that logic, you can find the distance between any two points, and therefore the lengths of the sides of any shape that they give you.

From there, the problems can twist and turn, but to find the area of any triangle or quadrilateral you need to have a relationship between the base and height of the shape, and that base-height relationship hinges on a right triangle (those two lengths must be perpendicular, meeting at 90-degrees). Again, use the coordinate plane to help you find right angles - the x and y axes are perfect places to find that relationship!

I hope that helps - I know that, at first, when I saw coordinate geometry I was deluged by flashbacks of my high school classes with TI-82 calculators and notebooks of graph paper, and I wasn't too thrilled about it. But because 90+% of coordinate geometry comes down to finding right angles, and those angles are provided by the axes, I quickly grew to love it (or at least love the fact that I could do these problems pretty quickly).