Question

The point (0,1) has the distance ____, from the line defined by y=-2x-1

How do you solve this?

I tried the pythagorean theorem but I don't think I did it right as I came out with the square root of two. Can someone please explain this to me.

Answer 1

The distance of a point (x0,y0) from a line L: Ax+By+C=0 is given by
Ax0+By0+C/√(A²+B²).

Here (0,1) ⇒ x0=0, y0=1.
L: y=-2x-1 ⇒ L: 2x+y+1 = 0
⇒ A=2, B=1, C=1.

So distance,
d = (2(0)+1+1)/√(2²+1²)
= 2/√(5)
= 2√(5)/5