# Thread: Analytical Geometry Question!!

1. ## Analytical Geometry Question!!

Given ABC> with vertices A(-7,3) B (-2,-3) C (4,2) verify that one median of the triangle is perpendicular to one of the sides.

I'm having trouble coming up with the correct answer to the question...I keep coming up with a decimal answer for the slope of the median...Help would be appreciated!!

2. Hello, Iux213!

Given $\displaystyle \Delta ABC$ with vertices $\displaystyle A(-7,3),\;B (-2,-3),\;C (4,2)$
Vverify that one median of the triangle is perpendicular to one of the sides.

I keep coming up with a decimal answer for the slope of the median.
Of course, you do . . . You're using your calculator, aren't you?

If you make a sketch, you'll see that the likely candidate
. . is the median from vertex $\displaystyle B$ to side $\displaystyle AC.$

The slope of $\displaystyle AC$ is: . $\displaystyle m_{_{AC}} \;=\;\frac{2-3}{4-(\text{-}7)} \;=\;-\frac{1}{11}$

The midpoint of is: .$\displaystyle M\left(-\frac{3}{2},\:\frac{5}{2}\right)$

Thje slope of $\displaystyle BM$ is: . $\displaystyle m_{_{BM}} \;=\;\frac{\frac{5}{2} - (\text{-}3)}{\text{-}\frac{3}{2}-(\text{-}2)} \;=\;11$

. . . Got it?

3. I'm with you sort of all the way...I understand why the slope of the median is what it is..I'm just not sure how you got to it, or how you determined the midpoint of AC...