GMAT Coordinate Geometry

A few months ago, I put together a list of ten GMAT math topics you must master, and included Coordinate Geometry as #10. It may not quite be the tenth most important topic on the GMAT Quantitative section, but it is far more important than many students give it credit for.

Typical Coordinate Geometry Lesson

If you take a test-prep course or read through a review book, you'll usually find three main issues within the topic of coordinate geometry:

• How to find slope
• The equation of a line
• The distance formula

All three of these things will come in handy, but they won't get you much further than a 500- or 550-level questions. As I'm saying all the time, the GMAT isn't about plugging numbers into formulas, it's about mathematical reasoning, and reasoning goes beyond simple equations.

What the GMAT Really Tests

Coordinate geometry has become more prevalent on the GMAT in the last several years, and I think I know why. As the test has gotten more challenging, the makers of the test have had to find ways to construct more difficult questions without requiring more content knowledge.

Think of an IQ test: IQ test questions rarely require any content knowledge at all, but they can get devilishly difficult. Many IQ test questions have to do with spatial reasoning--fitting pieces together, or seeing how shapes relate to one another. Coordinate geometry is one of the very few topics already on the GMAT that can put your spatial reasoning skills to the test.

Spatial Reasoning

In contrast to the plug-and-chug topics I mentioned above, here are some things that are more common on difficult coordinate geometry items:

• What does a line with a positive slope look like? How about a negative slope? What about a positive slope less than one? What's the slope of a very steep line?
• What's the slope of a line with negative x- and y-intercepts? How about a negative x-intercept and a positive y-intercept?
• If (m, n) is located in quadrant II, where is (-m, -n) located?

That's not an exhaustive list, by any means, but it does point in a different direction. When the GMAT is testing spatial reasoning, exact numbers are often beside the point--as with just about every other GMAT math topic, relationships are the key. That's one reason why these questions pop up on Data Sufficiency as much or more as they do in Problem Solving.

Study Guide

Total GMAT Math has a lengthy chapter on coordinate geometry, covering the basic topics I mentioned in addition to the more conceptual, spatial-reasoning- related issues I've listed. The book also includes several exercises and practice problems aimed at helping you think in the way that will help you nail these questions.

My Geometry: Challenge problem set also contains plenty of relevant practice, including many examples of how the GMAT will mix and match coordinate geometry with other geometry topics, such as right triangles and circles.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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