# Finding the midpoint given 2 points or coordinates tutorial

Given any 2 points $(x_1,y_1)$ and $(x_2,y_2)$, The x coordinate of the midpoint is the **half of the sum** of the x coordinates $x_1$ and $x_2$ and the y coordinate of the midpoint is **half of the sum** of the y coordinates $ y_1$ and $y_2$. Thus the formula of the midpoint is given by
$$ midpoint = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$
Procedure for calculating the midpoints

- State the formula
- Substitute for $ x_1,x_2,y_1 \text{ and } y_2 $
- Simplify and find the midpoint

### Worked Example

Calculate the midpoint of (2,1) and (8,9)

### Solution

Hind:you should understand that the first coordinate in a point is the x-coordinate and the second one is the y-coordinate. Then you denote the points as shown in the graphics below.

\begin{align} midpoint &= (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\
&= (\frac{2+8}{2},\frac{1+9}{2})\\
&= (\frac{10}{2},\frac{10}{2})\\
&= (5,5)\end{align}

## Midpoint Practice

If you would like to practice and gain more experience on calculating the midpoint given 2 points, then you can visit the

Midpoint Quiz Generator . You will have plenty of revision and fun. There will be infinite number of questions. Detailed solutions for incorrect response are provided. Go to the midoint quiz generator now and start revising. If you would like to verify your homework or assignment then you can visit the

Midpoint Calculator here . The midpoint calculator provides detailed solution for midpoint when 2 coordinates are entered. It can be used as a homework helper.

### Other Coordinate Geometry Tutorials

- Finding the equation of a straight line given 2 points tutorial
- Finding the gradient of a straight line given 2 points tutorial
- Finding the distance between 2 points tutorial