Question

Find the third vertex of a triangle if two of its vertices are at (-2,4)and (7,-3)and the centroid at (3,2)

Answer 1

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Answer 2

The third vertex of the triangle is (4, 5)

Let A($(x_{1}, y_{1} )$ = (-2, 4)

      B$(x_{2}, y_{2})$ = (7, -3)

      C$(x_{3}, y_{3})$ = ?

         centroid (G) = (3, 2)

          G = $(\frac{x_{1}+ x_{2} + x_{3} }{3} ,\frac{y_{1}+ y_{2} + y_{3}}{3} )$

        (3, 2) = $(\frac{-2+7+x_{3} }{3} , \frac{4-3+y_{3} }{3} )$

 $\frac{5+x_{3} }{3} = 3$          $\frac{1+y_{3} }{3} = 2$

        $5 + x_{3} = 9$                   $1 + y_{3} = 6$

        $x_{3} = 9 - 5 = 4$              $y_{3} = 6-1 = 5$

∴ $(x_{3} , y_{3}) = (4, 5)$