In this page centroid of triangle question4 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).

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).

Centroid of triangle question4 - Solution

Question 4 :

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

Solution:

Let the vertices be A (1,3) B (2,7) and C (5,4)

x₁ = 1 x₂ = 2 x₃ = 5

y₁ = 3 y₂ = 7 y₃ = 4

Formula:

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

= [ 1 + 2 + 5 ] / 3 , [ 3 + 7 + 4 ] / 3

= (3+5)/3 , (10+4)/3

= (8/3 , 14/3)

= (8/3,14/3)

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 question4

Question 8 :

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

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).