Mid-Point of Two Points

Summary

This math recipe will help you find the mid-point of two points, whose coordinates are known.

Mid Point

Skill Level

Easy

Time

Approx. 1 min

Ingredients

Coordinates of the two points: \(A(x_1, y_1)\) and \(B(x_2, y_2)\)

Method

To find the mid-point \(C\) of \(A\) and \(B\), we’ll simply plug their coordinates into the formula below:

\(C \equiv \left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right ) \)

This formula is sometimes called the Mid-Point Formula.

Examples

Example 1 Find the mid-point of \(P(4, 6)\) and \(Q(-2, 2)\).

Solution The figure shows the points  and  on the plane.

Mid Point

To find the mid-point \(R\), we’ll use the mid-point formula directly.

\(R \equiv \left ( \frac{4+(-2)}{2},\frac{6+2}{2} \right ) \)

\( \equiv \left ( \frac{2}{2},\frac{8}{2} \right ) \)

\( \equiv (2,4) \)

Example 2 Find the mid-point of \(A(-1, 5)\) and \(B(7, -3)\).

Solution The figure shows the points  and  on the plane.

Mid Point

To find the mid-point \(C\), we’ll again use the mid-point formula straight away.

\(C \equiv \left ( \frac{-1+7}{2},\frac{5+(-3)}{2} \right ) \)

\( \equiv \left ( \frac{6}{2},\frac{2}{2} \right ) \)

\( \equiv  (3,1) \)

That’s it for this recipe. Hope you found it helpful.

For more recipes, please visit www.doubleroot.in/recipes.

You can follow me on Instagram, Twitter, or Facebook to get all updates.

Scroll to Top