What is the distance between the line y=2x+3 and the point (1,0)

Answer 1

The way to do this problem is to compute the equation of the line through (1,0) and perpendicular to y=2x+3.

Then solve the system of two linear equations (the original equation and the perpendicular); this will give you the intersection of the two lines. Then compute the distance from (1,0) to the intersection point.

HOWEVER, there is a general solution to this problem which I will given you:

The distance from a point (x₁,y₁) to the line ax + by + c = 0 is given by

d = (ax₁ + by₁ + c)/sqrt(a² + b²).