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
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 .
With this information I found the equation of a line with the slope . Which is .
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?