Distance, midpoint, slope, section formula — Class 10 + Class 12 essentials
Reviewed by [email protected], Geometry Calculator Developer & Online Math Educator Last updated May 8, 2026
Coordinate geometry (analytic geometry) lets you compute geometric quantities from (x, y) coordinates instead of measurements. This is the complete NCERT Class 10 & Class 12 reference — covering the big four distance, midpoint, slope, and section formulas, plus the line equation forms (slope-intercept, point-slope, two-point) and the 3D distance extension.
| Name | Formula | Notes |
|---|---|---|
| Distance | d = √((x₂−x₁)² + (y₂−y₁)²) |
2D Pythagorean applied to coordinates. |
| Midpoint | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
Exact center of segment (x₁,y₁)–(x₂,y₂). |
| Slope | m = (y₂ − y₁) / (x₂ − x₁) |
Rise over run. Vertical lines: undefined. |
| Section Formula (internal) | P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) |
Point dividing segment in ratio m : n. |
| Slope-Intercept Form | y = mx + b |
m = slope, b = y-intercept. |
| Point-Slope Form | y − y₁ = m(x − x₁) |
Build a line from a point + slope. |
| Two-Point Form | (y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁) |
Build a line from two points. |
| Parallel Lines | m₁ = m₂ |
Equal slopes. |
| Perpendicular Lines | m₁ × m₂ = −1 |
Negative reciprocal slopes. |
| 3D Distance | d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²) |
Adds the z-axis. |
Plug in your numbers and get instant step-by-step results.