Find the minimum distance from the point (1, 2) to the line L = −4x − 1.

A point (x, y) on the line satisfies y = –4x – 1. The distance formula is

To find a minimum, find the derivative of D with respect to x.

This equals 0 when 34x + 22 = 0, or when x = –11/17, and y = –4(–11/17) – 1 = 27/17.

Therefore the minimum distance is ( (27/17 – 2)^1/2 + (–11/17 – 1)^1/2 )^1/2 =