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 (x_{1}y_{1}), (x_{2},y_{2}), and (x_{3},y_{3}) , 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

Question 2 :

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

Question 3 :

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

Question 4 :

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

Question 5 :

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

Question 6 :

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

Question 7 :

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

Question 10 :

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