Coordinate geometry calculator — distance, midpoint, slope and equation at once

How to use the coordinate geometry calculator

1. Enter the first point in x₁ and y₁.
2. Enter the second point in x₂ and y₂.
3. Read the list: Distance, Midpoint, Slope, Line equation, y-intercept and Angle of inclination.

What it does and when to use it

Coordinate geometry homework often asks several questions about the same pair of points: how long is the segment, where is its middle, how steep is it, and what is its equation? This tool answers all of them from one input, so it works well as a quick check after you have solved a problem by hand. It is also handy for proofs, such as showing that the diagonals of a quadrilateral bisect each other (same midpoint) or that two sides are parallel (same slope).

Each property has its own tool with the full method shown: the distance calculator, the midpoint calculator and the slope calculator, which also gives the x-intercept and perpendicular slope.

How it works

With Δx = x₂ − x₁ and Δy = y₂ − y₁, the tool computes:

• Distance: d = √(Δx² + Δy²)
• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)
• Slope: m = Δy/Δx
• y-intercept: b = y₁ − m·x₁, giving the line y = mx + b
• Angle of inclination: arctan(m) in degrees

If Δx is 0 the line is vertical, and the tool writes x = x₁ instead of y = mx + b.

Worked examples

All properties, step by step. Points (1, −2) and (7, 6).

1. Δx = 7 − 1 = 6 and Δy = 6 − (−2) = 8.
2. Distance: √(36 + 64) = √100 = 10.
3. Midpoint: ((1 + 7)/2, (−2 + 6)/2) = (4, 2).
4. Slope: 8/6 = 4/3 ≈ 1.333333333.
5. Intercept: b = −2 − (4/3)(1) = −10/3 ≈ −3.333333333.

The tool shows Midpoint: (4, 2), a distance of 10, Line equation: y = 1.333333333x − 3.333333333 and an angle of inclination of 53.130102°. In fraction form the line is y = (4/3)x − 10/3.

A horizontal segment. Points (−3, 5) and (2, 5) give distance 5, midpoint (−0.5, 5), slope 0 and the line y = 5.

A vertical segment. Points (4, 1) and (4, 7) give distance 6, midpoint (4, 4) and Line equation: x = 4, with the slope reported as undefined.

Limits and tips

• Two dimensions only. For points in space use the 3D distance calculator.
• If the two points are the same, the distance is 0 and the slope is reported as undefined.
• No units: answers follow whatever unit your coordinates use.
• Everything is worked out in your browser.