Coordinate Proof

Videos and lessons to help High School students learn how to use coordinates to prove simple geometric theorems algebraically.

For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2).

Common Core: HSG-GPE.B.4

Rectangle Proof on Coordinate Plane
Common Core State Standard G-GPE.4.
Proof that given coordinates on a coordinate plane form a rectangle.

Circle Proof on Coordinate Plane
Common Core State Standard G-GPE.4.
Proof that a coordinate lies on a circle with a given center and radius.

Introduction to Coordinate Proof
Strategies for placing figures in the coordinate plane
Use the origin as a vertex, keeping the figure in quadrant 1
Center the figure at the origin
Center a side of the figure at the origin
Use one or both axes as sides of the figure

Example 1: Positioning a Figure in the Coordinate Plane
Example 2: Writing a proof in Coordinate Geometry
Example 3: Assigning Coordinates to vertices
Example 4: Writing a Coordinate Proof.

How to Write Coordinate Proofs | Geometry How to Proof Help
This video models how to place a figure in the coordinate plane and how to write coordinate proofs.
Writing coordinate proofs requires a knowledge of the slope formula, the distance formula and the mid point formula.
Rectangle, Parallelogram, Trapezoid.

Triangles and Coordinate Proof
Placing triangles on the coordinate plane
1. Use the origin as a vertex or the center of a triangle.
2. Place at least one side of the triangle on an axis.
3. Keep the triangle within the first quadrant if possible.
4. Use coordinates that make computations as simple as possible.

Write a coordinate proof to show that a line segment joining the midpoints of the two sides of a triangle is parallel to the third side. (Midsegment Theorem)

Coordinate Proofs
Write a coordinate proof to show that the medians to the legs of an isosceles triangle are congruent.

Coordinate Proof for Quadrilaterals: Parallelogram, Square, Rectangle, Trapezoid.

Triangles and Coordinate Proof
Example: Place an isosceles triangle on the coordinate plane so that its sides are a units long and one side is on the positive x-axis.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.