PRACTICE PROBLEMS ON FINDING CENTRIOD OF A TRIANGLE WITH COORDINATES

Practice Problems on Finding Centriod of a Triangle with Coordinates :

In this section, we will see some practice questions on finding centriod of a triangle with coordinates.

Definition of centroid :

Consider a triangle ABC whose vertices are A(x₁, y₁), B(x₂ , y₂ ) and C(x₃ , y₃). Let AD, BE and CF be the medians of the triangle ABC.

The centroid G of the triangle with vertices A(x₁, y₁), B(x₂ , y₂ ) and C(x₃ , y₃) is

  =  [ (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3 ]

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 

Practice problems on finding centroid of a triangle

Question 1 :

Find the centroid of triangle whose vertices are (1, 10) (-7, 2) and (-3, 7).

Solution :

Let the vertices be A (1, 10) B (-7, 2) and  C (-3, 7)

x₁  =  1, x₂  =  -7, x₃  =  -3

y₁  =  10, y₂  =  2, y₃  =  7 

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

  =  [ 1+(-7)+(-3)/3 , (10+2+7) ]/ 3

  =  (1-7-3)/3, 19/3

  =  (-9/3 , 19/3)

  =  (-3, 19/3)

Question 2 :

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

Solution :

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

x₁  =  -1, x₂  =  2, x₃  =  2

y₁  =  -3, y₂ = 1, y₃  =  -4 

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

  =  [ ((-1)+2+2)/3, ((-3)+1+(-4))/3]

  =  [ (-1 + 4)/3, (-3+1-4)/3 ] 

  =  [3/3, (-7 + 1)/3   

  =  [ 1, (-6/3) ]

  =  (1, -2)

Question 3 :

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

Solution :

Let the vertices be A (1, 1) B (2, 3) and  C (-2, 2)

x₁  =  1, x₂  =  2, x₃  =  -2

y₁  =  1, y₂  =  3, y₃  =  2 

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

  =  [(1+2+(-2))/3, (1+3+2)/3]

  =  [ (3 - 2)/3 , (6/3) ]

  =  (1/3 , 2)

Question 4 :

Find the centroid of triangle whose vertices are (1, 3) (2, 7) and (5, 4).

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 

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)

Question 5 :

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

Solution :

Let the vertices be A (6, 7) B (2, -9) and  C (-4, 1)

x₁  =  6, x₂ = 2, x₃  =  -4

y1  =  7, y₂  =  -9, y₃  =  1 

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

  =  [ (6+2+(-4))/3 , (7+(-9)+1)/3

  =  (8 - 4)/3 , (8 - 9)/3 

  =  (4/3 , -1/3)

After having gone through the stuff given above, we hope that the students would have understood how to find practice problems on finding centriod of the triangle.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.