Posted by **Steve** on Friday, December 27, 2013 at 5:05pm.

Find the distance from the point (3, 2) to the line y = 3x + 2.

- Mathematics -
**Damon**, Friday, December 27, 2013 at 5:56pm
Well, you can memorize a formula that Reiny knows or you can figure it out.

First sketch a graph

find the line perpendicular to the given line that passes through the given point.

the slope of the given line is 3

so the slope of our perpendicular line is -1/3

so

y = -x/3 + b is our perpendicular line but what is b?

put in (3,2)

2 = -3/3 + b

b = 3

so

y = -x/3 + 3

Now where do these lines cross?

y = -x/3 + 3

y = 3 x + 2

------------- subtract

0 = - 10/3 x + 1

10 x = 3

x = 3/10

then

y = 9/10 + 20/10 = 29/10

so

d^2 = (3-3/10)^2 +( 2 - 29/10)^2

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