Question

The coordinates of the centroid of a
triangle whose vertices are (0, 6), (8,12)
and (8,0) is
(4,6)
(16,6
(5,7
(16/3, 6)​

Answer 1

Topic :-

Coordinate Geometry

Given :-

A triangle whose vertices are (0, 6), (8, 12)  and (8, 0).

To Find :-

Coordinates of the centroid of the traingle.

Concept Used :-

$\sf{Coordinates\:of\:the\:centroid\:of\:a\:triangle\:with}$

$\sf{vertices\:(x_1, y_1),(x_2, y_2)\:and\:(x_3, y_3)\:are\:given\:by:- }$

$\sf{(x,y)\equiv\left( \dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)}$

Solution :-

Considering,

$\sf {(0,6) \equiv (x_1,y_1)}$

$\sf {(8,12) \equiv (x_2,y_2)}$

$\sf {(8,0) \equiv (x_3,y_3)}$

Applying formula,

$\sf{(x,y)\equiv\left( \dfrac{0+8+8}{3},\dfrac{6+12+0}{3}\right)}$

$\sf{(x,y)\equiv\left( \dfrac{16}{3},\dfrac{18}{3}\right)}$

$\sf{(x,y)\equiv\left( \dfrac{16}{3},6\right)}$

Answer :-

$\sf {So, the\:coordinates\:of\:centroid\:of\:given\:triangle\:would\:be\:\left( \dfrac{16}{3},3 \right)}$

$\sf{which\:is\:\bold{4^{th}\:option}\:here.}$

Additional Information :-

Centroid always remain inside the triangle.

The centroid is present at two-third of median from vertex.

The orthocentre, centroid and circumcentre of any triangle are collinear. The line on which all three points lie is called as Euler line.

In equilateral triangle, all these three centres coincide.

A triangle can have only one centroid.