The Perpendicular Distance from a Point to a Line

In this video, I demonstrate how to calculate the perpendicular distance from a point (2, -1) to the line described by the equation y = 3x + 1.

In order to calculate this distance, we use the "Perpendicular Distance Formula", given by:

d=\frac{\left | Am+Bn+C \right |}{\sqrt {A^2+B^2}}

where:

• A, B and C are the constants of the standard form linear equation: Ax + By + C = 0
• m is the x-coordinate of the point of interest
• n is the y-coordinate of the point of interest.

Thus, rearranging the equation of our line from y = 3x + 1 to 3x - y + 1 = 0 gives the values (A, B, C) = (3, -1, 1) and our point of interest (m, n) = (2, -1). We can substitute these values into the perpendicular distance formula to calculate the perpendicular distance.