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A(h,-6),B(2,3) and C(-6,k) are the coord...

A(h,-6),B(2,3) and C(-6,k) are the coordinates of vertices
of a triangle whose centroid is G(1,5). Find h and k.

Text Solution

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`A(h,-6),B(2,3),C(-6,k)` and `G(1,5)`.
Suppose the coordinates of point A are `(x_(1),y_(1))`, coordinates of point B are `(x_(2),y_(2))` coordiates of point C are `(x_(3),y_(3))` and coordinates of point G are `(x,y)`
Here `x_(1)=h,y_(1)=-6, x_(2)=2, y_(2)=3,x_(3)=-6,y_(3)=k,x-1` and `y=5`.
By centroid formula,
`x=(x_(1)_+x_(2)+x_(3))/3, y=(y_(1)+y_(2)+y_(3))/3`
`:.1=(h+2+(-6))/3, :.6=(-6+3+k)/3`
`:.3=h-4, :.15=-3+k`
`:.h-3+4, :.k=15+3`
`:.h=7, :.k=18`
`h=7` and `k=18`
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