Coordinate Geometry: Line Properties

Analyze the relationship between two points: Distance, Slope, Midpoint, and Equation.

Point 1

x₁

y₁

Point 2

x₂

y₂

Properties

Distance7.2111

Midpoint(1, 3)

Slope (m)0.6667

Equationy = 0.67x + 2.33

Coordinate Geometry

Coordinate geometry (or analytic geometry) is the study of geometry using a coordinate system. This calculator derives the fundamental properties of the line segment connecting two points (x₁, y₁) and (x₂, y₂).

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Pro Tips

The slope 'm' represents the steepness of the line: Rise over Run.
The equation is given in slope-intercept form y = mx + b, or x = c for vertical lines.
The midpoint is effectively the average of the coordinates.

Fun Facts

"René Descartes initially published his ideas on this subject in 1637 as an appendix to 'Discourse on the Method'."
"Coordinate geometry bridged the gap between Algebra and Geometry."

Formula: d = √((x₂-x₁)²+(y₂-y₁)²), m = (y₂-y₁)/(x₂-x₁)

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