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Question
Find the third vertex of a ΔABC if two of its vertices are B(-3,1) and C (0,-2) and its centroid is at the origin
Solution
Two vertices of ΔABC are B(-3,1) and C (0,-2) .Let the third vertex be A (a, b). Then, the coordinates of its centroid are
`((-3+0+a)/3, (1-2+b)/3)`
i.e `((-3+a)/3 , (-1+b)/3)`
But it is given that the centroid is at the origin, that is G (0,0) Therefore
`0= ((-3+a)/3,0=(-1+b)/3)`
⇒ 0=-3+a,0=-1+b
⇒3= a,1=b
⇒ a=3, b=1
Therefore, the third vertex of ΔABC A(3,1).
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