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Question
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Solution
We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be(x,y).
The co-ordinates of other two vertices are (−3, 1) and (0, −2)
The co-ordinate of the centroid is (0, 0)
We know that the co-ordinates of the centroid of a triangle whose vertices are
`(x_1,y_1),(x_2,y_2),(x_3,y_3)`is
`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`
So,
`(0,0)=((x+0-0)/3,(y+1-2)/3)`
Compare individual terms on both the sides-
`(x-3)/3=0`
So,
x=3
Similarly,
`(y-1)/3=0`
So,
y=1
So the co-ordinate of third vertex (3,1)
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