Finding distances and midpoints

If we want to find the distance between two points on a number line we use the distance formula:

$$AB=\left | b-a \right |\; or\; \left | a-b \right |$$

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Example

Point A is on the coordinate 4 and point B is on the coordinate -1.

$$AB=\left | 4-(-1) \right |=\left | 4+1 \right |=\left | 5 \right |=5$$

If we want to find the distance between two points in a coordinate plane we use a different formula that is based on the Pythagorean Theorem where (x₁,y₁) and (x₂,y₂) are the coordinates and d marks the distance:

$$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$$

The point that is exactly in the middle between two points is called the midpoint and is found by using one of the two following equations.

Method 1: For a number line with the coordinates a and b as endpoints:

$$midpoint=\frac{a+b}{2}$$

Method 2: If we are working in a coordinate plane where the endpoints has the coordinates (x₁,y₁) and (x₂,y₂) then the midpoint coordinates is found by using the following formula:

$$midpoint=\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$$

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Video lesson

Find the midpoint of the line segment.