Hey!

I am having trouble finding the minimum distance from a point to a line. Here is the question:

For each of the following, find the distance from Q(3,-2) to each line.

a) 3x - 2y - 6 = 0

** Solution**
First I put into the form y = mx + b (because I am more familiar with this)

I now know that the slope of the line is

, which means that the line perpendicular to it has the slope of

.

correct
With this information I found the equation of a line with the slope

. Which is

.

you changed your mind here though,
I then found where the equations

and

intersect by solving the system of equations. I got the point

.

So I now know the point on the equation closest to the point Q. So all I need to do is find the distance between them. So:

This is my final answer.

The book says the answer should be

.

I am doing exactly what the textbook is telling me to do. What am I doing wrong?