# What is the definition of a coordinate proof? And what is an example?

##### 1 Answer

See below

#### Explanation:

Coordinate proof is an algebraic proof of a geometric theorem. In other words, we use numbers (coordinates) instead of points and lines.

In some cases to prove a theorem algebraically, using coordinates, is easier than to come up with logical proof using theorems of geometry.

For example, let's prove using the coordinate method the Midline Theorem that states:

Midpoints of sides of any quadrilateral form a parallelogram.

Let four points

Midpoint

Midpoint

Midpoint

Midpoint

Let's prove that

As we see, the slopes of

Analogously, slopes of

So, we have proven that opposite sides of quadrilateral