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Question
The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is
Options
(0, 0)
(4, 7)
(7, 4)
(7, 7)
(4, 4)
Solution
(4, 7)
Let A(4, 8) and B(−2, 6) be the given vertex. Let C(h, k) be the third vertex.
The centroid of \[\bigtriangleup\] ABC is \[\left( \frac{4 - 2 + h}{3}, \frac{8 + 6 + k}{3} \right)\].
It is given that the centroid of triangle ABC is (2, 7).
\[\therefore \frac{4 - 2 + h}{3} = 2, \frac{8 + 6 + k}{3} = 7\]
\[ \Rightarrow h = 4, k = 7\]
Thus, the third vertex is (4, 7).
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