SOLUTION: Please help, I've been stuck on this question all day. Decide whether or not the points are the vertices of a right triangle. (-9,-4), (-5,-4), )-5,1)

Algebra ->  Points-lines-and-rays -> SOLUTION: Please help, I've been stuck on this question all day. Decide whether or not the points are the vertices of a right triangle. (-9,-4), (-5,-4), )-5,1)      Log On


   

Question 181501: Please help, I've been stuck on this question all day.
Decide whether or not the points are the vertices of a right triangle.
(-9,-4), (-5,-4), )-5,1)
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
you only need prove that the line from (-5,1) to (-5,-4) lets call this line a is perpendicular to the line from (-9,-4) to (-5,-4)lets call this line b
:
In order to do this we need to find the slopes. remember perpendicular lines have slopes that are negative recipricals of each other
:
problem here is one line is vertical so undefined slope. the other is horizontal line which is slope zero. that by itself really proves lines are perpendicular . but teacher probably wants further proof
:
so we will use distances
:
we know the distance of line a is 5 and we know the distance of line b is 4
:
so 4%5E2%2B5%5E2=c%5E2 so c=sqrt%2841%29 meaning that for this to be a right triangle the hypothenuse has to be sqrt%2841%29
:
lets use the distance formula for line c which is from point (-5,1) to (-9,-4)
:
D=sqrt%28%28-5-%28-9%29%29%5E2%2B%281-%28-4%29%29=4%5E2%2B5%5E2=41%29
:
so D=sqrt%2841%29
:
using pathagorean theorem and the distance formula we have proved this is a right triangle