Question

the coordinates of the vertical of a triangle are 3, - 1 and 10, 7 and 5, 3 find the coordinates of its centroid​

Answer 1

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G(6,3)

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step-by-step explanation:

Let,

the triangle be ∆ABC

and,

the vertices be,

A = ($x_1,y_1$) = (3,-1)

B = ($x_2,y_2$ ) = (10,7)

C = ($x_3,y_3$) = (5,3)

Now,

we know that,

Centroid of a triangle is the point of intersection of all the medians.

let,

the centroid be denoted by G(x,y)

Now,

we know that,

For the coordinate of centroid, G

x = $\frac{x_1+x_2+x_3}{3}$

and

y = $\frac{y_1+y_2+y_3}{3}$

So,

putting the respective values,

we get,

x = (3+10+5)/3 = 18/3 = 6

and

y = (-1+7+3)/3 = 9/3 = 3

HENCE,

the coordinate of centroid is

G(6,3)

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