Question

Find the centroid of the triangle whose vertices are $A\left( {7,\, - 8} \right),\,\,B\left( { - 9,\,7} \right),\,\,C\left( {8,13} \right)$.

Answer 1

Hint: We will make use of the concept of the centroid of the triangle and solve this question
Centroid of triangle G for
$x = \dfrac{{{x_1} + {x_2} + {x_3}}}{3}$ …(i)
$y = \dfrac{{{y_1} + {y_2} + {y_3}}}{3}$ …(ii)

Complete step by solution:
 Let coordinate of (g) = (x, y)
{$x_1$} = 7 & {$y_1$} = - 8
{$x_2$} = - 9 & {$y_2$} = 7
{$x_3$} = 8 & {$y_3$} = 13
Centroid of $x = \dfrac{{{x_1} + {x_2} + {x_3}}}{3}$
$ = \dfrac{{7 - 9 + 8}}{3}$
$ = \dfrac{{15 - 9}}{3}$
$ = \dfrac{6}{3}$
$ = 2$
Centroid of $y = \dfrac{{{y_1} + {y_2} + {y_3}}}{3}$
$ = \dfrac{{ - 8 + 7 + 13}}{3}$
$ = \dfrac{{ - 8 + 20}}{3}$
$ = \dfrac{{12}}{3}$
$ = 4$
Centroid of triangle $G = \left( {2,4} \right)$


Note: Before you solve the problem you know about the centroid of a triangle, and its formula .It will help you to get the correct answer and students should put the exact value of ${x_1},{x_2},{x_3}and{y_1},{y_2},{y_3}$in the formula to calculate the centroid.