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In Delta ABC, G(-4, -7) is the centroid ...

In `Delta ABC, G(-4, -7)` is the centroid of `Delta ABC.` If `A(-14, -19) and B(3,5)` then find co-ordinates of C.

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`A(-14,-19),B(3,5)` and `G(-4,-7)` Suppose the coordinates of point A are `(x_(1),y_(1))`, coordinates of point B are `(x_(2),y_(2)),` coordinates of point C are `(x_(3),y_(3))` and coordinates of point are `(x,y)`.
Here `x_(1)=-14,y_(1)=-19, x_(2)=3, y_(2)=5, x=-4, y=-7`.
By centroid formula,
`x=(x_(1)+x_(2)+x_(3))/3, y=(y_(1)+y_(2)+y_(3))/3`
`:.-4=(-14+3+x_(3))/3,:.-7=(-19+5+y_(3))/3`
`:.-12=-11+x_(3),:.-21=-14+y_(3)`
`:.x_(3)=-12+11,:.y_(3)=-21+14`
`:.x_(3)=-1, :.y_(3)=-7`
The coordinates of C are `(-1,-7)`.
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