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Coordinate Geometry Calculator

Five modes for every coordinate geometry problem. Enter points and see distances, midpoints, slopes, line equations, circles, and triangle properties with an interactive graph that updates in real time. All calculations run in your browser.

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d=(3−0)2+(4−0)2=5d = \sqrt{(3 - 0)^2 + (4 - 0)^2} = 5
M=(0+32,  0+42)=(1.5,  2)M = \left(\frac{0 + 3}{2},\; \frac{0 + 4}{2}\right) = (1.5,\; 2)
Distance
5
Midpoint
(1.5, 2)

Reference Guide

Distance Formula

The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is derived from the Pythagorean theorem.

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

The midpoint is the point exactly halfway between two given points.

M=(x1+x22,  y1+y22)M = \left(\frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2}\right)

Slope and Line Equations

The slope measures steepness. It equals the ratio of vertical change (rise) to horizontal change (run).

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Three common forms for a line equation

y=mx+b(slope-intercept)y = mx + b \quad \text{(slope-intercept)}
y−y1=m(x−x1)(point-slope)y - y_1 = m(x - x_1) \quad \text{(point-slope)}
Ax+By=C(standard)Ax + By = C \quad \text{(standard)}

Circle Equations

A circle with center (h,k)(h, k) and radius rr can be written in two forms.

(x−h)2+(y−k)2=r2(standard)(x - h)^2 + (y - k)^2 = r^2 \quad \text{(standard)}
x2+y2+Dx+Ey+F=0(general)x^2 + y^2 + Dx + Ey + F = 0 \quad \text{(general)}

Where D=−2hD = -2h, E=−2kE = -2k, and F=h2+k2−r2F = h^2 + k^2 - r^2. Three non-collinear points uniquely determine a circle.

Triangle Properties

The shoelace formula gives the area of a triangle from its vertex coordinates.

A=12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣A = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|

Every triangle has four classic centers. The centroid (G) is the average of the vertices. The circumcenter (O) is equidistant from all vertices. The incenter (I) is equidistant from all sides. The orthocenter (H) is where the altitudes meet.