Question

Find the distance from point A(15, -21) to the line 5x +2y = 4

Answer 1

The distance from a point to a line is
distance(ax+by+c=0,(x0,y0)) = abs(ax0+by0+c)/sqrt(a^2+b^2)
So first convert the formula for the line to standard form
5x+2y=4
5x+2y-4=0

a=5, b=2, c=-4, x0=15, y0=-21

abs(5*15+2*(-21)-4)/sqrt(5*5+2*2)
= abs(75-42-4)/sqrt(25+4)
= 29/sqrt(29)
= sqrt(29)
= 5.385165 (approximately)