How to Find the Centroid of a Triangle ?
Here we are going to see how to find the centroid of a triangle.
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
Example 1 :
Find the centroid of the triangle whose veritices are A(6, −1), B(8, 3) and C(10,−5).
Centroid of triangle = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3
= (6 + 8 + 10)/3, (-1 + 3 - 5)/3
= (24/3, -3/3)
= (8, -1)
Example 2 :
If the centroid of a triangle is at (−2, 1) and two of its vertices are (1, −6) and (−5, 2), then find the third vertex of the triangle
Centroid of the triangle = (-2, 1)
(x1 + x2 + x3)/3, (y1 + y2 + y3)/3 = (-2, 1)
Let (a, b) be the vertex of the triangle.
(1 - 5 + a)/3, (-6 + 2 + b)/3 = (-2, 1)
(-4 + a)/3, (-4 + b)/3 = (-2, 1)
Equating the x and y coordinates.
(-4 + a)/3 = -2
-4 + a = -6
a = -6 + 4
a = -2
(-4 + b)/3 = 1
-4 + b = 3
b = 3 + 4
b = 7
Hence the missing vertex is (-2, 7).
After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Centroid of a Triangle"
Apart from the stuff given in "How to Find the Centroid of a Triangle", if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Different forms equations of straight lines
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions