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Find the equation of the medians of the ...

Find the equation of the medians of the triangle ABC whose vertices are `A(2,5)B(-4,9)a n d\ C(-2,-1)dot`

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The vertices of `triangle ABC` are `A=(2,5), B(-4,9) and C(-2,-1)`.
Let D,E,F be the midpoints of BC, CA and AB respectively.
Then these points are `D=((-4-2)/(2),(9-1)/(2)), e((-2+2)/(2),(-1+5)/(2))and F((2-4)/(2),(5+9)/(2))`
`D(-3,4),E(0,2) and F(-1,7)`.
Thus, AD,BE and CF are the medians of `triangle of ABC`..
Equation of meidan AD is `(y-5)/(x-2)=(4-5)/(-3-2) Rightarrow (y-5)/(x-2)=(1)/(5) `
`Rightarrow 5(y-5)=x-2`
`x-5y+23=0`
Equation of median BE is `(y-9)/(x+4)=(2-9)/(0+4) Rightarrow (y-9)/(x+4)=(-7)/(4)`
`Rightarrow 4(y-9)+7(x+4)=0`
`Rightarrow 7x+4y-8=0`
`"Equation of median CF is "(y+1)/(x+2)=(7+1)/(-1+2) Rightarrow (y+1)=8(x+2)`
`Rightarrow 8x-y+15=0`
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