Question

An easy way to find the distance between a point (x,y) and a line (ax + by = c)?

Answer 1

you use the distance formula:\[d={\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\]

Answer 2

right, but that's from two points. so if you have an equation like y = 2x + 6 and a point, say, (3,4) then how would you find the difference?

Answer 3

*distance, sorry

Answer 4

convert the line from ax+by=c form to y=mx+b form and graph it

Answer 5

help him out @sami-21 :)

Answer 6

the distance formula from point (x,y) to line ax+by+c =0 is
\[\Large d=\frac{|ax+by+c|}{\sqrt{a^2+b^2}}\]
for example if i have to find the distance from (3,2) to line 3x+4y+9=0
here a=3, b=4, c=9 , x=3,y=2
so distance will be
\[\Large d=\frac{|(3(3)+4(2)+9|}{\sqrt{(3)^2+(4)^2}}=\frac{|26|}{\sqrt{25}}=\frac{26}{5}\]

Answer 7

@MSMR is it ok now ?

Answer 8

Thank you! Wow, that must have taken a lot of time to make on the equation editor. Thank you so much, I'll be sure to memorize that formula. Thanks to you and @yummydum!

Answer 9

you are welcome :)

Answer 10

i didnt do much but youre welcome! :)

Answer 11

credit goes to @sami-21 :D