Question

The coordinates of the mid-points of the sides of a triangle are (4, 3), (6, 0) and (7, —2).

Find the coordinates of the centroid of the triangle.​

Answer 1

Given: Coordinates of the mid - points of the sides of a triangle are (4, 3), (6, 0) and (7, -2).

To find: The centroid of the triangle.

Answer:

Since the mid - points of the sides are given, we can directly move on the finding the centroid of the triangle.

Formula to do so:

$\tt P(x,\ y)\ =\ \bigg(\dfrac{x_1\ +\ x_2\ +\ x_3}{3},\ \dfrac{y_1\ +\ y_2\ +\ y_3}{3}\bigg)$

From the points given, we have,

$\tt x_1\ =\ 4\\\\x_2\ =\ 6\\\\x_3\ =\ 7\\\\y_1\ =\ 3\\\\y_2\ =\ 0\\\\y_3\ =\ -2$

Using them in the formula,

$\tt Centroid\ =\ \bigg(\dfrac{4\ +\ 6\ +\ 7}{3},\ \dfrac{3\ +\ 0\ -\ 2}{3}\bigg)\\\\\\Centroid\ =\ \bigg(\dfrac{17}{3},\ \dfrac{1}{3}\bigg)$

Answer 2

Answer:

( 17 / 3 , 1 /3 )

Step-by-step explanation:

Given :

Co-ordinates of the mid point of the side of triangle are :

( 4 , 3 ) , ( 6 , 0 ) and ( 7 , - 2 ).

Let the Centroid of the triangle be P :

We know :

Centroid of the triangle P =  ( ( x₁ + x₂ + x₃ ) / 3 , ( y₁ + y₂ + y₃ ) / 3 )

P = ( ( 4 + 6 + 7 ) / 3 , ( 3 + 0 - 2 ) / 3 )

P = ( 17 / 3 , 1 / 3 )

Therefore , Centroid of the triangle is ( 17 / 3 , 1 / 3 ).