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# Distance and midpoint calculator

This online calculator will compute and plot the distance and midpointof a line segment. The calculator will generate a step-by-step explanation on how to obtain the results.

Distance and midpoint calculator
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 Distance (default) Midpoint
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examples
example 1:ex 1:
Find the distance between the points $(–5, -1)$ and $(3, 4)$.
example 2:ex 2:
Find the distance between the points $\left( \frac{3}{4} , -3 \right)$ and $\left( -\frac{13}{4}, 5\right)$.
example 3:ex 3:
Find the midpoint M between $(–3, 5)$ and $(4, –2)$.
example 4:ex 4:
Find the midpoint M between $\left( \frac{1}{2}, \frac{5}{3} \right)$ and $\left( -\frac{4}{3}, –2\right)$.

## How to find distance between two points ?

To find distance between points $A(x_A, y_A)$ and $B(x_B, y_B)$, we use formula:

$${\color{blue}{ d(A,B) = \sqrt{(x_B - x_A)^2 + (y_B-y_A)^2} }}$$

Example:

Find distance between points $A(3, -4)$ and $B(-1, 3)$

Solution:

In this example we have: $x_A = 3,~~ y_A = -4,~~ x_B = -1,~~ y_B = 3$. So we have:

\begin{aligned} d(A,B) & = \sqrt{(x_B - x_A)^2 + (y_B-y_A)^2} \\ d(A,B) & = \sqrt{(-1 - 3)^2 + (3 - (-4) )^2} \\ d(A,B) & = \sqrt{(-4)^2 + (3 + 4 )^2} \\ d(A,B) & = \sqrt{16 + 49} \\ d(A,B) & = \sqrt{65} \\ d(A,B) & \approx 8.062 \end{aligned}

Note: use this calculator to find distance and draw graph.

## How to find midpoint of line segment ?

The formula for finding the midpoint $M$ of a segment, with endpoints $A(x_A, y_A)$ and $B(x_B, y_B)$, is:

$${\color{blue}{ M~\left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right) }}$$

Example:

Find midpoint of a segment with endpoints $A(3, -4)$ and $B(-1, 3)$.

Solution:

As in previous example we have: $x_A = 3,~~ y_A = -4,~~ x_B = -1,~~ y_B = 3$~. So we have:

\begin{aligned} M~\left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right) \\ M~\left(\frac{-1 + 3}{2}, \frac{3 - 4}{2}\right) \\ M~\left(\frac{2}{2}, \frac{-1}{2}\right) \\ M~\left(1, \frac{-1}{2}\right) \end{aligned}

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