Formulas from plane analytic geometry
Distance between two points and
Slope of line joining two points and
Equation of line joining two points and
where is the intercept on the axis, i.e. intercept.
Equation of line in terms of intercept and intercept
Normal form for equation of line
where = perpendicular distance from origin to line
and α = angle of inclination of perpendicular with
with positive axis.
General equation of line
Distance from point to line
where the sign is chosen so that the distance is nonnegative.
Angle between two lines having slopes and
Lines are parallel or coincident if and only if
Lines are perpendicular of and only if
Area of triangle with vertices at
where the sign is chosen so that the area is nonnegative. If the area is zero the points all lie on a line.