Slope, Midpoint & Distance
From two points: slope, angle, distance, midpoint, the line in slope-intercept, point-slope and standard form, both intercepts and the perpendicular bisector.
Δx, Δy, slope and its angle, the distance and midpoint, y = mx + b, the point-slope and integer standard forms, x- and y-intercepts, the perpendicular slope and bisector.
Example: (1, 2) and (4, 8): slope 2 at 63.4°, distance √45 = 6.708, midpoint (2.5, 5), y = 2x, standard form 2x − y = 0, perpendicular bisector y = −0.5x + 6.25.
Two points,
one line, six forms.
The formulas, how the standard form clears fractions, and what happens on vertical and horizontal lines.
The measurements
Slope m = Δy ÷ Δx and its angle atan2(Δy, Δx); distance √(Δx² + Δy²) (Pythagoras); midpoint the average of the coordinates. These are the same for either order of the points except the sign of the angle.
The equations
Slope-intercept y = mx + b with b = y₁ − m·x₁; point-slope y − y₁ = m(x − x₁); standard form Ax + By = C with integer coefficients, obtained by writing m and b as fractions (denominators up to 10⁶ from the coordinates you typed) and clearing them, then dividing by the common factor so A is positive. Intercepts follow from b and −b/m. The perpendicular bisector has slope −1/m and passes through the midpoint.
Special cases
Δx = 0 gives a vertical line x = c with undefined slope; Δy = 0 a horizontal line y = c whose perpendicular is vertical. Identical points define no line and are refused. Values are rounded only for display. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- m = Δy/Δx; distance √(Δx² + Δy²); midpoint ((x₁ + x₂)/2, (y₁ + y₂)/2); standard form by clearing rational coefficients (denominators ≤ 10⁶); vertical lines as x = c
Last reviewed 21 September 2026. How results are checked: How we verify.