The coordinate geometry calculator computes all properties of the line through two points: distance, midpoint, slope, y-intercept, standard form, angle of inclination, and the perpendicular bisector equation.
Coordinate Geometry Calculator
Perpendicular Bisector
Step-by-Step
How to Use the Coordinate Geometry Calculator
Coordinate geometry (analytic geometry) connects algebra and geometry by representing geometric objects as equations. Two points in the Cartesian plane define a unique line, and this calculator finds all of its properties.
Distance and Midpoint
Distance: d = √((x₂−x₁)² + (y₂−y₁)²) — the Pythagorean theorem applied to the coordinate differences. Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2) — the average of the coordinates.
Slope and Line Equations
Slope: m = (y₂−y₁)/(x₂−x₁). Slope-intercept form: y = mx + b, where b = y₁ − m×x₁. Standard form: Ax + By = C (integer coefficients, A positive). Angle of inclination: θ = arctan(m) in degrees.
Perpendicular Bisector
The perpendicular bisector passes through the midpoint and has slope −1/m (the negative reciprocal). It's used to find circumcenters of triangles and the set of points equidistant from both endpoints.
FAQ
What is the distance formula?
The distance between two points (x₁,y₁) and (x₂,y₂) is d = √((x₂−x₁)² + (y₂−y₁)²). This comes directly from the Pythagorean theorem applied to the right triangle formed by the two points and their projection.
How do I find the slope between two points?
Slope m = (y₂−y₁)/(x₂−x₁), often described as 'rise over run'. A positive slope goes up-right, negative goes down-right. Undefined slope means a vertical line (x₁=x₂). Zero slope means horizontal (y₁=y₂).
What is the slope-intercept form?
Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept (where the line crosses the y-axis). Given two points, calculate m first, then use one point to solve for b: b = y₁ − m×x₁.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
What is the perpendicular bisector?
The perpendicular bisector of a line segment is the line that passes through the midpoint and is perpendicular to the segment. If the original slope is m, the perpendicular slope is −1/m. The perpendicular bisector is used in circumcenter calculations and geometric proofs.