SOLUTION: Triangle QRS has vertices Q(-4,-1)R(-1,3)S(5,-3). Write the equation of the line containing the altitude through point R. Need Help studying for quiz! Would be nice for the answe

Algebra ->  Points-lines-and-rays -> SOLUTION: Triangle QRS has vertices Q(-4,-1)R(-1,3)S(5,-3). Write the equation of the line containing the altitude through point R. Need Help studying for quiz! Would be nice for the answe      Log On


   

Question 802591: Triangle QRS has vertices Q(-4,-1)R(-1,3)S(5,-3).
Write the equation of the line containing the altitude through point R.
Need Help studying for quiz! Would be nice for the answer and complete work!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The altitude through point R is the line that passes through R and is perpendicular to the line QS.

The slope of the line QS is
.

The product of the slopes of two perpendicular lines is -1.
So the slope of a line perpendicular to QS is
m=%28-1%29%2F%28%28-2%2F9%29%29=%28-1%29%2A%28-9%2F2%29=9%2F2

A point, +%22%28+x+%2C+y+%29%22+, on a line with slope m that passes through +P+%28+x%5BP%5D+%2C+y%5BP%5D+%29+ satisfies
m=%28y-y%5BP%5D%29%2F%28x-x%5BP%5D%29 <--> y-y%5BP%5D=m%28x-x%5BP%5D%29
(The equation y-y%5BP%5D=m%28x-x%5BP%5D%29 is called the point-slope form of the equation of the line).
Applying that to point +R+%28+-1+%2C+3+%29+ and slope m=9%2F2 we get
y-3=%289%2F2%29%28x-%28-1%29%29 --> y-3=%289%2F2%29%28x%2B1%29 --> y-3=%289%2F2%29x%2B9%2F2 --> y=%289%2F2%29x%2B9%2F2%2B3 --> highlight%28y=%289%2F2%29x%2B15%2F2%29