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Question
Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.
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 (1, 2) and (3, 5)
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+1+3)/3,(y+2+5)/3) or ((4+x)/3,(7+y)/3)`
Compare individual terms on both the sides -
`(4+x)/3 = 0
⇒ 4 + x = 0
⇒ x = -4
and
`(7+y)/3=0`
⇒ 7 + y = 0
⇒ y = -7
So the co-ordinate of third vertex (-4, -7)
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