Centroid of Triangle Question8





In this page centroid of triangle question8 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).        centroid of triangle question8



(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)




Centroid of triangle question8 - Solution

Question 8 :

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

Solution:

Let the vertices be A (1,3) B (-7,6) and  C (5,-1)

x₁ = 1           x₂ = -7              x₃ = 5

y₁ = 3           y₂ = 6               y₃ = -1 

Formula:

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

                               = [ 1 + (-7) + 5 ] / 3 , [ 3 + 6 + (-1) ] / 3

                               = (6 - 7)/3 , (3 + 6 - 1)/3 

                               = [-1/3 , (9-1)/3]   

                               = [-1/3 , 8/3]   

                               = (-1/3,8/3)      


Question 9 :

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



(A) (4, 3)
(B) (3 , 1)
(C) (3 , 5)




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)




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Centroid of Triangle Question8 to Analytical Geometry