Coordinate geometry calculator

Formula

How it works

Distance uses the Pythagorean theorem on the horizontal and vertical gaps between the points. The midpoint averages the x-coordinates and the y-coordinates separately. The slope is the vertical change divided by the horizontal change; it is undefined for a vertical line.

Worked example

The same calculation with the default values:

• x₁ 1
• y₁ 2
• x₂ 7
• y₂ 10

1. distance = √((7 − 1)² + (10 − 2)²) = 10
2. midpoint = ((1 + 7) ÷ 2, (2 + 10) ÷ 2)
3. slope = (10 − 2) ÷ (7 − 1) = 1.333333

Result: Distance: 10 · Midpoint x: 4 · Midpoint y: 6

Common mistakes

• Subtracting coordinates in the wrong order inconsistently between x and y (e.g. x₂−x₁ but y₁−y₂) - the order must be consistent in both the distance and slope formulas, though the distance formula's squaring hides this particular mistake while the slope formula does not.
• Confusing midpoint with distance - the midpoint is a point (an x,y location halfway between), not a length; they answer different questions and use different formulas.
• Treating a vertical line's undefined slope as zero - a slope of zero describes a horizontal line, the opposite case; a vertical line's slope is undefined, not zero.