Distance and Midpoint Formulas Examples

Suppose that M is the midpoint of WX. What are the coordinates of point X?

We want to find the point X, which we'll give coordinates (x, y). If M is the midpoint of WX, we can use the midpoint formula and solve for x and y.

This gives us two different equations.

Solving these two equations gives coordinates X = (-2, -3).

Is M the midpoint of YZ?

We compute the midpoint using the midpoint formula.

Since these are not the coordinates of point M, we can conclude that M is not the midpoint of the segment.

What is the length of MW?

We use the two-dimensional distance formula to find the distance from M to W.

The length of MW is 5 units.

Again assuming M is the midpoint of WX, what is the length of WX?

We could use the distance formula again, but we could instead use the fact that MW is half as long as WX. Since we know the length of MW is 5 from the previous example, that means WX measures 10 units.