Coordinate geometry – think regular geometry, with an extra step or two

Coordinate geometry problems can throw off the best of test-takers, and with good reason – who among us has worked with a coordinate plane since high school? (I definitely hadn’t when I began studying for the GRE). There’s little reason to fear coordinate geometry, though: Once you become comfortable accurately drawing figures on a place, then you just need to apply the same skills that you use on regular geometry problems. Take this GRE Quantitative Comparison question, for example:

We’re given two of the triangle’s three vertices, and we know that point B is in quadrant III since both of its coordinates are negative. If we draw that out, it looks like this:

Once we have a clearer idea of what we’re looking at, it can be tempting to throw in the towel and choose answer choice (D). We know that y, the y-coordinate of point B, is negative, but how can we tell whether it’s greater or less than -5, the value in Quantity B? But we don’t have to give up just yet – we have one more piece of information that might be able to help us.

If we go back to the centered information, we see that the total area of the triangle is 12. We can tell from our sketch that the base of the triangle is 4. If we plug our base and area into the formula for the area of a triangle, A = ½*b*h, we get 12 = ½(4)(h). If we continue solving for h, we get:

12 = 2h

6 = h

So we know that the triangle is 6 units “tall”, and we have our value for y: -6. So even though we don’t know exactly where point B is, it doesn’t matter – we were still able to find the y-coordinate’s value. Drawn into our graph, that looks like this:

Now all that’s left is to compare it to the value in Quantity B: -6 is less than -5, so Quantity B is greater and we have our final answer.

The test-writers could have posed a very similar question without testing coordinate geometry: We could just have easily have been told that we had a triangle with a base of 4 and an area of 12, and been asked to determine how the height related to a value in Quantity B. By making us plot the information on a plane instead, the writers are hoping that you’ll either be daunted by the very idea of coordinate geometry, or make a mistake when you draw the figure. Don’t fall for the traps – just sketch carefully, and you’ll be well on your way to gaining points on GRE Test Day!