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Mike MᶜGarry

Big Ideas of SAT Coordinate Geometry

This is Mike McGarry, Magoosh’s GMAT Expert. As you may know, the GMAT is the entrance exam for business school. Believe or not, folks studying to be the business leaders of tomorrow don’t necessarily know any more math that you do! You see, some folks get to the end of whatever their last required math class is, say Algebra II, and they bail on math. These folks go through the rest of high school and college blissfully ignoring mathematics, and then when they want to go to graduate school or business school, they suddenly have to look at math again! If I may give you some advice: even if you hate math, even if you think all math is worse than a trip to a sadistic dentist, please keep up some kind of math practice, even just arithmetic, if you have any plans of doing more school after college. It’s as if your brain has a “math muscle” – as with any muscle, it can be hard to exercise it, but it’s even harder to let it atrophy and then discover that you need it!

Coordinate Geometry

If Twitter had been invented in the 1630’s, Mr. René Descartes (1596 – 1650) would have gotten even more acclaim for his brilliant idea. Of course, like many brilliant ideas, it is utterly simple in retrospect: take two number lines and put them at right angles to make the x-y coordinate plane. Sometimes the x-y plane is called the “Cartesian plane,” in honor of Mr. Descartes.


This was a truly remarkable breakthrough in mathematics because it created a deep connection between Algebra (equations) and Geometry (shapes & pictures): every equation with x & y gives us some kind of shape/picture in the x-y plane! These two branches of math had been completely separate and virtually unrelated until Mr. Descartes’ discovery. This paved the way for other, even more brilliant, interconnections between equations and shapes, such as Mr. Sir Isaac Newton‘s idea of calculus. Fortunately, you don’t need to know about Mr. Newton’s ideas on the SAT, but you do need to understand the big ideas of Coordinate Geometry.

Useful GMAT Blogs for SAT Students

Here are a few GMAT blogs that discuss precisely the things you need to know for the SAT:

1) Quadrants of the x-y plane
Chris also talks about this in his blog on Coordinate Geometry Basics.

2) Special properties of the line y = x
This discusses some of those quick tricks that the SAT-writers love!

3) Distance between two points
Let your friend and mine, Mr. Pythagoras, convince you that memorizing a Distance Formula is a huge waste of time!

4) Lines & Slopes in the x-y plane
An important topic.

5) Midpoints, Parallel & Perpendicular Lines
Another important topic.

If you want some practice questions, this next blog has some additional questions that could be on the SAT:

6) Coordinate Geometry Practice Questions
Ignore question #2: it is Data Sufficiency question, a question type unique to the GMAT; you don’t need to know about these at all for the SAT. Just skip that question.

If you really want to challenge yourself, take a look at this one:

7) Challenging Coordinate Geometry Practice Questions
If you can handle those eight questions, you will be able to handle anything the SAT will throw in your direction about coordinate geometry.


Finally, here’s an SAT practice question on Coordinate Geometry.

Let us know about your experience of reading GMAT blogs to prepare for the SAT!


About Mike MᶜGarry

Mike creates expert lessons and practice questions to guide GMAT students to success. He has a BS in Physics and an MA in Religion, both from Harvard, and over 20 years of teaching experience specializing in math, science, and standardized exams. Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets.

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