Centroid of Triangle Question6

In this page centroid of triangle question6 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 question6

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

Centroid of triangle question6 - Solution

Question 6 :

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

Solution: Let the vertices be A (3,4) B (2,-1) and  C (4,-6)

x₁ = 3           x₂ = 2              x₃ = 4

y₁ = 4           y₂ = -1            y₃ = -6

Formula:

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

= [ 3 + 2 + 4 ] / 3 , [ 4 + (-1) + (-6) ] / 3

= (5 + 4)/3 , (4 - 1 - 6)/3

= [9/3 , (4-7)/3]

= [9/3 , -3/3]

= (3,-1)

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)

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)