Question

a triangle has a vertices at A(6,7) B(2,-9) and C(-4,1) find the slope of it median​

Answer 1

Answer:

Let a triangle has vertices A ≡ (6, 7) , B ≡ (2, -9) and C ≡ (-4, 1) and D , E and F are the midpoint of BC , CA , AB respectively. So, AD , BE and CF are the medians of triangle ABC.

So, first of all we have to find points D , E and F

D is the midpoint of BC .

so, D ≡ [ (2 -4)/2 , (-9 + 1)/2 ] [from midpoint section formula]

D ≡ (-1 , -4)

E is the midpoint of CA.

so, E ≡ [ (-4 + 6)/2 , (1 + 7)/2 ]

E ≡ (1 , 4)

F is the midpoint of AB

F ≡ [ (6 + 2)/2 , (7 - 9)/2 ]

F ≡ (4 , -1)

Now, A ≡ ( 6, 7) and D≡ (-1 , -4)

Slope of median AD = (-4 - 7)/(-1 - 6) = 11/7

similarly, slope of median BE = (4 + 9)/(1 - 2) = -13

slope of median CF = (1 + 1)/(4 + 4) = 1/4

Step-by-step explanation:

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