Find a Perpendicular Line Through a Point - Calculator
A calculator to find the equation of a line that is perpendicular to a given line and passing through a point.
Equation of a Line Perpendicular to Another Line and Through a point P
The slope \( m \) of line L given by the equation \( A x + B y = C \) is given by
\[ m = - \dfrac{A}{B} \]
If two lines are perpendicular, the product of their slopes is equal to \(-1\)
\[ m \cdot m' = - 1 \]
Hence the slope of the line perpendicular to line L is given by
\[ m' = \dfrac{-1}{- \dfrac{A}{B}} = \dfrac{B}{A} \]
The equation, in point slope form, of a line parallel to line L and through point P (a,b) is given by
\[ y - b = \dfrac{B}{A} (x - a) \]
How to use the calculator
1 - Enter the coordinates of the point through which the line passes.
2 - Enter A, B and C the coefficients of the the given line defined as follows.
\[ A x + B y = C \]
3 - press "enter". The answer is an equation, in slope intercept form, of the line perpendicular to the line entered and passing through the point entered .
The coordinates and coefficients may be entered as fractions, integers or decimals.(see examples below).
Solve problems manually and check your answer using this calculator.
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