# 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

1. State the formula
2. Substitute for $x_1,x_2,y_1 \text{ and } y_2$
3. 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

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