Distance Of A Point From A 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.

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.