Question

The vertices of a triangle are (0, 0), (3, 0) and (0, 4). The centroid of the triangle is?

Answer 1

The vertices of the triangle are as follows :-

A(0,0)

B(3,0)

C(0,4)

To find the centroid of a triangle with known vertices, we can use two ways :-

1)Long-method in which median is divided into 2:1 ratio and the division point is found by using section formula.

2)Shortcut method :-

There is a direct formula to find centroid of the triangle.

The formula is as follows :-

$\boxed{\red{\sf{\bold{G=\dfrac{x_1 +x_2 +x_3}{3}, \dfrac{y_1 +y_2 +y_3}{3}}}}}$

We will be solving it by using the second process :-

X1 = 0

X2 =3

X3 =0

Y1 =0

Y2 = 0

Y3 = 4

$=G= \frac{0 + 3 + 0}{3}, \frac{0 + 0 + 4}{3} \\ \\ \\ = 1, \frac{4}{3}$

Hence,

Centroid of the triangle given is as follows :-

$\boxed{\bold{1,\dfrac{4}{3}}}$

Answer 2

$<font Color = "purple" >$

Hello billa ❤

Here is your answer :-

Given :- vertices of triangle (0,0), (3,0) ,(0,4)

To find :- Centroid of traingle..

Let's solve . ..

Centeroid =( X1 + X2 + X3 )/3 and (Y1 +Y2 +Y3) /3

Ox= (0+3+0)/3

= 1

Oy=(0+0+4)/3

Oy=1.3

Centeroid = (1,1.3)