Question

Find the distance from the point (1,2) to the line y=2x-1

Answer 1

distance
`= (\bf 1)/(√(\bf 5))` units

Explanation:

distance
`= (|ax_0+by_0+c|)/(√(a^2+b^2))`

Given equation is
`y=2x-1`

it can be written as
`2x-y-1=0`

here
`a=2, y=-1, c=-1` and the point
`(x_0, y_0)` is
`(1, 2)`

distance
`= (|2(1)+(-1)(2)-1|)/(√(2^2+1^2))`

distance
`= (|2-2-1|)/(√(4+1))`

distance
`= (|-1|)/(√(5))`

distance
`= (1)/(√(5))` units