Centroid of Triangle Question9





In this page centroid of triangle question9 we are going to see solution of first question of the quiz.

Definition of centroid:

The simple definition for centroid of a triangle is, the point of concurrency of the medians.

If the coordinates of A,B and C are (x1y1), (x2,y2), and (x3,y3) , then the formula to determine the centroid of the triangle given by

In the above triangle , AD, BE and CF are called medians. All the three medians AD, BE and CF are intersecting at G. So  G is called centroid of the triangle

Question 1 :

Find the centroid of triangle whose vertices are (1,10) (-7,2) and (-3,7).



(A) (2 , 8)
(B) (-3 , 19/3)
(C) (2 , 5)




Question 2 :

Find the centroid of triangle whose vertices are (-1,-3) (2,1) and (2,-4).



(A) (1 , -2)
(B) (-3 , 3)
(C) (1 , -5)




Question 3 :

Find the centroid of triangle whose vertices are (1,1) (2,3) and (-2,2).



(A) (-2 , -6)
(B) (4/3 , 9)
(C) (-1/3 , 2)




Question 4 :

Find the centroid of triangle whose vertices are (1,1) (2,3) and (-2,2).



(A) (8/3 , 14/3)
(B) (-5/3 , 7/3)
(C) (1/3 , -5/3)




Question 5 :

Find the centroid of triangle whose vertices are (6,7) (2,-9) and (-4,1).



(A) (4/3, -1/3)
(B) (-7/3 , 1/3)
(C) (1/3 , -5/3)




Question 6 :

Find the centroid of triangle whose vertices are (3,4) (2,-1) and (4,-6).



(A) (3, -1)
(B) (-7 , 3)
(C) (1 , -5)




Question 7 :

Find the centroid of triangle whose vertices are  (5,6) (2,4) and (1,-3).



(A) (4/3, -1/3)
(B) (8/3 , 7/3)
(C) (4/3 , 5/3)




Question 8 :

Find the centroid of triangle whose vertices are  (1,3) (-7,6) and (5,-1).  centroid of triangle question9



(A) (-4/3, 5/3)
(B) (-1/3 , 7/3)
(C) (-1/3 , 8/3)




Centroid of triangle question9 - Solution

Question 9 :

Find the centroid of triangle whose vertices are  (1,1) (3,4) and (5,-2).

Solution:

Let the vertices be A (1,1) B (3,4) and  C (5,-2)

x₁ = 1           x₂ = 3                x₃ = 5

y₁ = 1           y₂ = 4               y₃ = -2 

Formula:

Centroid of a triangle = (x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3

                               = [ 1 + 3 + 5 ] / 3 , [ 1 + 4 + (-2) ] / 3

                               = (4 + 5)/3 , (5 - 2)/3 

                               = [9/3 , 3/3]   

                               = [3 , 1]   

                               = (3,1)      

Question 10 :

Find the centroid of triangle whose vertices are  (-3,-9) (-1,6) and (3,9).



(A) (-5, -1)
(B) (8 , 7)
(C) (-1 , 2)














Centroid of Triangle Question9 to Analytical Geometry