Distance Between Point And Line

The equation of the line is given by: Let the common parameter be . Then, parametrize the coordinates of the point on the line: The distance between the point and a point on the line is given by the formula: Setting this equal to , we solve for to find the coordinates of the required point on the line.

The equation of the line is given in symmetric form: Let the common parameter be . Then, parametrize the coordinates of a point on the line as: Now, the distance between the point and a point on the line must be minimized to find the foot of the perpendicular. Using the formula for distance between two points: Minimizing this distance, we solve for that gives the minimum distance. After solving, the coordinates of the foot of the perpendicular are found.