I get 13/5.
Using vector arithmetic
(1,-1) - (-3,-4) = (4,3) perpendicular is (-3,4)
(2,3) - (1,-1) = (1,4)
(-3,4)*(1,4) / 5 = (-3 + 16) / 5 = 13/5
Check your work.
Hello !! This is a simple problem, but I'm not getting the right results. I am getting 9/5 but the text says that the correct answer is 13/5.
Problem:
Determine the distance of the point (2,3) from the line joining the points (-3,-4) and (1,-1).
Are you getting the same answer as mine ?
I assume you are trying to find the minimum distance from that point to the line.
First, find the equation of the line:
and .
So and
.
The minimum distance from the point to the line will occur when that distance is perpendicular to the line.
Drawing this distance gives another straight line. Since it is perpendicular to the other line, their gradients multiply to give .
So
.
You know that lies on your new line, so
.
Now to find where the point where the two lines cross:
.
When ,
.
So the two lines cross at .
Now all that's left is to find the distance between and .
.
So the minimum distance from the line joining and to the point is units.