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
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)
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Aug 28, 24 08:09 PM
Aug 28, 24 07:59 PM
Aug 28, 24 07:50 PM