Question

Which is the distance between the point with the coordinates (1, 2) and the line with the equation 2x-3y=-2

Answer 1

The formula for the distance between the point (x1,y1) and the line of the equation ax + by + c = 0 is
d = |ax1 + by1 + c|
--------------------
sqrt(a^2 + b^2)

so here we have

d = | 2*1 +(-3)2 + 2|
---------------------
sqrt(2^2 + (-3)^2)

= 2 / sqrt 13

= 2 sqrt13 / 13