Question

The $ .......... $ is also called the center of gravity of the triangle.
 $ \left( a \right){\text{ median}} $
 $ \left( b \right){\text{ vertex}} $
 $ \left( c \right){\text{ centroid}} $
 $ \left( d \right){\text{ altitude}} $

Answer 1

Hint: In this, we have the intersection point of its medians. It is a point which is at a distance of two-thirds the length of the median from the respective vertex. In this, it will be divided into the ratio of $ 2:1 $ . By using these points we can answer this question.

Complete step-by-step answer:
Center of gravity of a triangle will be its centroid which is the intersection point of its medians.
So in the coordinate geometry having the vertices,
 $ \left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\& \left( {{x_3},{y_3}} \right) $
then the coordinates of the centroid or also we can say it the center of gravity of triangle will be given by
 $ C.G = \left( {\dfrac{{{x_1} + {x_2} + {x_3}}}{3},\dfrac{{{y_1},{y_2},{y_3}}}{3}} \right) $
The focal point of gravity of a triangle is known as the centroid. For this drawing medians from the three vertices onto the contrary side. Where the three medians meet is the centroid. It is a point a ways off of two-thirds of the length of the middle from the particular vertex. The other one-third is the distance of the centroid from the side to which it is associated. That is the centroid separated the middle in the proportion of $ 2:1 $ . It is otherwise called the barycent.
So, the correct answer is “Option c”.

Note: For solving this type of question we have to know the definitions and the concept of the terms used in it. In practice we can also find it, suppose we have a triangular plate then we should have to try to balance the plate on our finger and when we get that point then it will be the centroid of that triangle.