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Calculators :: Analytic Geometry :: Distance and midpoint

This online calculator will compute and plot the distance and midpoint for two points in two dimensions. The calculator will generate a step-by-step explanation on how to obtain the results.

Distance and midpoint calculator

This calculator will return the result representing the midpoint and distance between two points
You can enter either integers (10), decimal numbers(10.12) or FRACTIONS(10/3). Important: The form will NOT let you enter wrong characters (like *, (, ), y, p, ...)

Distance Midpoint
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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 ?

distance and midpoint diagram

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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