Question

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

Answer 1

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