Question

The centroid of the triangle whose vertices are A (4,-6), B (3,-2), C (5, 2) is

Answer 1

Hint: We will use the formula for centroid of the triangle. The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle

Complete step-by-step answer:

Let vertices of triangle are $A\left( {x,{y_1}} \right),B\left( {{x_2},{y_2}} \right),C\left( {{x_3},{y_3}} \right)$ then centroid of triangle is given by $ = \left( {\dfrac{{{x_1} + {x_2} + {x_3}}}{3},\dfrac{{{y_1} + {y_2} + {y_3}}}{3}} \right)$
Now given points are $A(4, - 6),B(3, - 2),C(5,2)$
$x$ Coordinate of Centroid of triangle $ = \dfrac{{4 + 3 + 5}}{2} = \dfrac{{12}}{2} = 6$
$y$ Coordinate of centroid of triangle $ = \dfrac{{ - 6 - 2 + 2}}{2} = \dfrac{{ - 6}}{2} = - 3$
Therefore, centroid of $\Delta ABC = (6, - 3)$

Additional Information: Centroid is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle separates the median in the ratio of 2: 1. It can be found by taking the average of x- coordinate points and y-coordinate points of all the vertices of the triangle. Centroid of a Square is the point where the diagonals of the square intersect each other is the centroid of the square. As we all know, the square has all its sides equal. Hence it is easy to locate the centroid in it. See the below figure, where O is the centroid of the square
The properties of the centroid are as follows:
1.The centroid is the centre of the object.
2.It is the centre of gravity.
3.It should always lie inside the object.
4.It is the point of concurrency of the medians.


Note: Centroid - It is the mean position of all points in all of the coordinate directions. It can be defined also for a triangle as the intersection of three medians of the triangle (each median connecting a vertex with the midpoint of opposite side).