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Coordinate Geometry Formulas & Calculators

Understand coordinate geometry formulas with explanations, examples and interactive tools.

Coordinate Geometry

Distance Between Points

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance between two points in a plane.

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Coordinate Geometry

Midpoint

\(M=(\frac{x_1+x_2}2,\frac{y_1+y_2}2)\)

Midpoint of a line segment.

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Coordinate Geometry

Slope

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Rate of change of y with x for nonvertical line.

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Coordinate Geometry

Section Formula

\(P=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})\)

Point dividing segment internally in ratio m:n.

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Coordinate Geometry

Circle Equation

\((x-h)^2+(y-k)^2=r^2\)

Circle with centre (h,k) and radius r.

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Coordinate Geometry

Straight Line Slope Intercept

\(y=mx+c\)

Line with slope m and y-intercept c.

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Coordinate Geometry

Parabola Standard Equation

\(y^2=4ax\)

Right/left opening parabola based on sign of a.

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Coordinate Geometry

Ellipse Standard Equation

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Ellipse centered at origin for a,b>0.

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