Centroid of Triangle Question10





In this page centroid of triangle question10 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).                centroid of triangle question10



(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).



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




Centroid of triangle question10 - Solution

Question 10 :

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

Solution:

Let the vertices be A (-3,-9) B (-1,6) and  C (3,9)

x₁ = -3           x₂ = -1              x₃ = 3

y₁ = -9           y₂ = 6               y₃ = 9 

Formula:

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

                               = [ (-3) + (-1) + 3 ] / 3 , [ (-9) + 6 + 9 ] / 3

                               = [-3 - 1 + 3 )/3 , (-9 + 6 + 9 )/3 

                               = [(-4 + 1)/3 , (-9 + 15)/3]   

                               = [-3/3 , 6/3]   

                               = (-1,2)      

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Centroid of Triangle Question10 to Analytical Geometry