⌖Coordinate Geometry Calculator

Distance, midpoint, section formula, lines, intersections, perpendicular distance, triangles, and circles — with coordinate-plane plots and step-by-step solutions.

Distance Between Two Points

Calculates the horizontal change, vertical change, vector displacement, exact square-root form, and decimal distance.

Steps
Classic Examples
Distance3–4–5 segment Distancediagonal across quadrants Midpointequal split Sectiondivide AB in 2:3 Linepositive slope Linevertical line Intersectperpendicular lines Intersectparallel lines Point–Lineshortest distance Triangleisosceles example Triangleright triangle Circlecentre and point Circleradius five Circumcircleright-triangle circle Circumcirclegeneral points
Steps Modes
None  Answer and visual only.
Summary  Methods as compact pills.
Detailed  Openable calculation steps with substitutions.
Operations Guide
AB — Distance
Length, displacement vector, radical form
M:P — Midpoint & Section
Midpoint and internal ratio point
y=mx+b — Line Equation
Slope, forms, direction, intercepts
ℓ₁∩ℓ₂ — Intersection
Cramer solution and smaller line angle
d(P,ℓ) — Point–Line Distance
Shortest distance and perpendicular foot
△ABC — Triangle
Lengths, shoelace area, centroid, angles
(x−h)² — Circle
Centre, radius, equations, measurements
○ABC — Circumcircle
Circle through three non-collinear points
Key Formulas
Distance\(d=\sqrt{\Delta x^2+\Delta y^2}\)
Midpoint\(M((x_1+x_2)/2,(y_1+y_2)/2)\)
Slope\(m=\Delta y/\Delta x\)
Line\(Ax+By+C=0\)
Point–line\(d=|Ax_0+By_0+C|/\sqrt{A^2+B^2}\)
Shoelace\(K=\frac12|\sum x_iy_{i+1}-y_ix_{i+1}|\)
Centroid\(G((x_1+x_2+x_3)/3,...)\)
Circle\((x-h)^2+(y-k)^2=r^2\)
Circumradius\(R=abc/(4K)\)
Input Tips
  • Enter decimals, negatives, or whole numbers.
  • Each point needs an x- and y-coordinate.
  • Use two distinct points for every line.
  • Use non-collinear points for a three-point circle.
  • For section P, ratio m:n means AP:PB.
  • Vertical lines have undefined slope, but valid equations.
  • The visual plot adjusts to the calculated values.
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