Straight Lines
6.0 Foot of perpendicular from a point to a line
6.0 Foot of perpendicular from a point to a line
The foot of perpendicular drawn from a point $P({x_1},{y_1})$ on a line $ax+by+c=0$ can be found out using the following steps:
- Draw the perpendicular from $P$ to the line which meets at $M$ as shown in the figure.
- Since $PM$ is perpendicular to the given line, find the slope of $PM$ using the condition ${m_1} \times {m_2} = - 1$.
- Use point-slope form to find the equation of line $PM$ and solving it with $ax+by+c=0$ to find the coordinates of $M$.
