directed distance from a line

Question

Find the distance from the line 5x= 12y+26 to the point P1(3,-5) P2(-4,1) & P3(9,0)

Answer 1

Given line equaton 5x = 12y+26

Subtract 5x from each side.

5x-5x = 12y+26-5x

-5x+12y+26 = 0

Compare it line equation ax+by+c = 0

a = -5, b = 12, c = 26

Distance to a line from the point is = (ax1+by1+c)/(sqrt(a^2+b^2))

Distance to given line from P1(3,-5) = (-5*3+12*-5+26)/[sqrt(25+144)]

= (-15-60+26)/13 = -49/13

Distance to given line from P2(-4,1) = (-5*-4+12*1+26)/(sqrt(25+144))

= (20+12+26)/13

= 58/13

Distance to given line from the point P3(9,0) = (-5*9+12*0+26)/(sqrt(25+144))

= (-45+0+26)/13

= 19/13