Find the distance between the point (2,-5) and the line 3x-5y+13= 0

For the distance between a point and a line we use the
formula:

D = l ax1 + by1 + c l/
sqrt(a^2+b^2)

Such that: ax+by+c = 0 is the line and
(x1,y1) is the point.

In our example, we have the line
3x-5y + 13 = 0

==> a =3    b= -5    c =
13

and the point (2,-5) ==> x1= 2   y1=
-5

Let us
substitute:

==> D= l 3*2 + -5*-5 + 13 l /
sqrt(9+25)

           = l 6+25 + 13l /
sqrt(34)

          =
44/sqrt34

Then the distance between the point
and the line is 44/sqrt34.