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Two-Point Geometry Calculator

Distance, midpoint, slope, and line equation from any two points

Enter two coordinates and this calculator finds the four most common results in coordinate geometry: the distance between the points, the midpoint, the slope, and the equation of the line through them.

The graph updates live as you change the points. You can see the segment, the full line, the midpoint, and the horizontal and vertical changes that create slope and distance.

This is useful for algebra, analytic geometry, graphing linear equations, and checking homework step by step.

Graph

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FAQ

What does this two-point calculator find?
It calculates the distance, midpoint, slope, and the equation of the line through the two points. It also plots the segment, the full line, the midpoint, and the horizontal and vertical changes on the graph so you can connect each formula to the picture.
What is the slope formula for two points?
For points (x_1, y_1) and (x_2, y_2), the slope is m = \frac{y_2 - y_1}{x_2 - x_1}. The numerator is the vertical change and the denominator is the horizontal change. If x_1 = x_2, the line is vertical, the horizontal change is zero, and the slope is undefined.
How do you find the midpoint of two points?
Average the x-values and the y-values: M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right). This gives the point exactly halfway between the two endpoints, both horizontally and vertically. On the graph, it is the center point of the segment joining the two coordinates.
How do you find the distance between two points?
Use the distance formula: d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. This comes directly from the Pythagorean theorem: the horizontal and vertical changes form the legs of a right triangle, and the segment between the points is the hypotenuse.

Related Topics

Distance Between Two PointsSlope of a LineLinear Equations