Question

The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is

विकल्प

• (0, 0)

• (4, 7)

•  (7, 4)

• (7, 7)

• (4, 4)

Answer 1

(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).