Mathematics
posted by Steve on .
Find the distance from the point (3, 2) to the line y = 3x + 2.

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 = (33/10)^2 +( 2  29/10)^2