Math Guide

Geometry Coordinate Proofs

In the seventeenth century, the French mathematician Rene Descartes applied algebraic principles to geometric situations. This blending of algebra and geometry is referred to as analytic geometry.  Because this process often involves placing geometric figures in a coordinate plane, it is also more commonly known as coordinate geometry.


Coordinate geometry proofs employ the use of formulas such as the Distance Formula, the Slope Formula and/or the Midpoint Formula as well as postulates, theorems and definitions.


Tips for Coordinate Geometry Proofs


  • Organize your work and label everything. Do not just perform calculations all over the place and leave your teacher to figuring out what is what (because we won’t!).
  • Label your algebra statements clearly
  • so,for example, if you’re going to prove the parallelogram (A(-5,-1),B(-4,3),C(8,0) and D(7,-4)) by definition, one thing you’ll need to do is find the slope of BC. When you show that, write something like slope BC="(3-0)/(-4-8)" = -1/4

More Tips for Coordinate Geometry Proofs


  • You must refer to your calculations and provide a summary/proof statement when done. For example, if you have just finished finding 4 slopes and are now ready to say that it is a parallelogram, then you would finish with something like this:
    • because both have slopes = -1/4
    • because both have slopes = 4/1
    • Since both pairs of opp. sides are , it’s a  by def.
  • Do not turn nice fractions like ¾ into decimals – reduce all fractions
  • You must show algebraic work for things in your proofs – you cannot just simplify, for example, lookat the graph paper and write down the point, where it looks like 2 lines intersect – you must use some algebraic way to find the point.

If the above tips are followed then its very easy to do Coordinate Geometry Proofs.