Question

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

Answer 1

Answer:

centroid(10/3,-1)

Step-by-step explanation:

formula of centroid of triangle is (x1+x2+x3)/3 and (y1+y2+y3)/3

x1=6,x2=0,,x3=4

y1=2,y2=0,y3= -5

x=(x1+x2+x3)/3

   6+0+43

   10/3

y=(y1+y2+y3)/3

  2+0-5/3

   -3/3

  -1

x=10/3

y=-1

centroid(10/3,-1)

Answer 2

Given: A triangle formed by the points (6, 2), (0, 0) and (4, -5).

To find: The centroid.

Answer:

Formula to find the centroid:

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

From the points given, 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,

$\tt Centroid\ =\ \Bigg(\dfrac{6\ +\ 0\ +\ 4}{3},\ \dfrac{2\ +\ 0\ +\ -5}{3}\Bigg)\\\\\\Centroid\ =\ \Bigg(\dfrac{10}{3},\ \dfrac{-3}{3}\Bigg)\\\\\\Centroid\ =\ \Bigg(\dfrac{10}{3},\ -1\Bigg)$

Therefore, the centroid of the triangle formed by the points (6, 2), (0, 0) and (4, -5) is (10/3, -1).