Question

Find the centroid of a triangle, whose vertices are (6, 2), (0, 0) and (4, – 5).

Answer 1

Given: The vertices of the triangle are (6, 2), (0, 0) and (4, -5).

To find: The centroid.

Answer:

Centroid formula:

$\tt \Bigg( \dfrac{x_1\ +\ x_2\ +\ x_3}{3},\ \dfrac{y_1\ +\ y_2\ +\ y_3}{3}\Bigg)$

From the data we have,

$\tt x_1\ =\ 6\\\\x_2\ =\ 0\\\\x_3\ =\ 4\\\\y_1\ =\ 2\\\\y_2\ =\ 0\\\\y_3\ =\ -5$

Using them in the formula,

$\tt \Bigg(x,\ y\Bigg)\ =\ \Bigg(\dfrac{6\ +\ 0\ +\ 4}{3},\ \dfrac{2\ +\ 0\ +\ -5}{3}\Bigg)\\\\\\\Bigg(x,\ y\Bigg)\ =\ \Bigg(\dfrac{10}{3},\ \dfrac{-3}{3}\Bigg)$

Therefore, the centroid of the triangle is (10/3, -1).

Answer 2

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• The Vertices of triangle are (6,2) , (0,0) and (4,-5)

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$

Find the Centroid of triangle = ?

$\large{\underline{\underline{\bf{FORMULA\:USED:-}}}}$

$\large\bf\red{Centroid = \frac {x_1 + x_2 + x_3 }{3},\frac{y_1 + y_2 + y_3}{3}}$

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

$\bf{x_1 = 6}$ ⠀⠀⠀⠀ $\bf{y_1 = 2}$

$\bf{x_2 = 0}$ ⠀⠀⠀⠀ $\bf{y_2 = 0}$

$\bf{x_3 = 4}$⠀⠀⠀⠀ $\bf{y_3 = -5}$

❍ We have given that the vertices of triangle are (6,2), (0,0) and (4,-5)

☞ On putting the values in formula, we get

$\implies$$\rm{ Centroid =\frac{6+0+4}{3},\frac{2+0+(-5)}{3}}$

$\implies$$\rm{ Centroid =\frac{6+0+4}{3},\frac{2+0-5}{3}}$

$\implies$$\rm{Centroid =\large\frac{10}{3},\cancel\frac{-3}{3}}$

$\implies$$\rm{Centroid =\frac{10}{3},-1}$

Hence, the Centroid of the triangle is $\bf{\frac{10}{3}}$, $\bf{-1}$