## CENTROID OF A TRIANGLE WORKSHEET

Problem 1 :

Find the centroid of a triangle whose vertices are the points (8, 4), (1, 3) and (3, -1).

Problem 2 :

Find the centroid of a triangle whose vertices are the points (6, -1), (8, 3) and (10, -5).

Problem 3 :

If a triangle has its centroid at (4, 3) and two of its vertices are (2, -1) and (7, 8), find the third vertex.

Problem 4 :

If the centroid of a triangle is (-2, 1) and two of its vertices are (1, -6) and (-5, 2), then find the third vertex.

Problem 5 :

Master gave a triangular plate with vertices (5, 8), (2, 4) and (8, 3) and a stick to a student. He wants to balance the plate on the stick. Can you help the boy to locate that point which can balance the plate ? ## Solutions

Problem 1 :

Find the centroid of a triangle whose vertices are the points (8, 4), (1, 3) and (3, -1).

Solution :

Formula to find centroid of a triangle is

= [(x+ x+ x3)/3, (y+ y+ y3)/3]

x1  =  8, x2  =  1 and x3  =  3

y1  =  4, y2  =  3 and y3  =  -1

=  [(8 + 2 + 3)/3, (4 + 3 - 1)/3]

=  (12/3, 6/3)

=  (4, 2)

So, the centroid of the given triangle is (4, 2).

Problem 2 :

Find the centroid of a triangle whose vertices are the points (6, -1), (8, 3) and (10, -5).

Solution :

Formula to find centroid of a triangle is

= [(x+ x+ x3)/3, (y+ y+ y3)/3]

x1  =  6, x2  =  8 and x3  =  10

y1  =  -1, y2  =  3 and y3  =  -5

Then,

=  [(6 + 8 + 10)/3, (-1 + 3 - 5)/3]

=  (24/3, -3/3)

=  (8, -1)

So, the centroid of the given triangle is (8, -1).

Problem 3 :

If a triangle has its centroid at (4, 3) and two of its vertices are (2, -1) and (7, 8), find the third vertex.

Solution :

Let (a, b) be the third vertex.

Centroid of the triangle  =  (4, 3)

[(x+ x+ x3)/3, (y+ y+ y3)/3]  =  (4, 3)

x1  =  2, x2  =  7 and x3  =  a

y1  =  -1, y2  =  8 and y3  =  b

Then,

[(2 + 7 + a)/3, (-1 + 8 + b)/3]  =  (4, 3)

[(9 + a)/3, (7 + b)/3]  =  (4, 3)

Equate the coordinates of x and y.

 (9 + a)/3  =  49 + a  =  12a  =  3 (7 + b)/3  =  37 + b  =  9b  =  2

So, the third vertex is (3, 2).

Problem 4 :

If the centroid of a triangle is (-2, 1) and two of its vertices are (1, -6) and (-5, 2), then find the third vertex.

Solution :

Let (a, b) be the third vertex.

Centroid of the triangle  =  (-2, 1)

[(x+ x+ x3)/3, (y+ y+ y3)/3]  =  (-2, 1)

x1  =  1, x2  =  -5 and x3  =  a

y1  =  -6, y2  =  2 and y3  =  b

Then,

[(1 - 5 + a)/3, (-6 + 2 + b)/3]  =  (-2, 1)

[(-4 + a)/3, (-4 + b)/3]  =  (-2, 1)

Equate the coordinates of x and y.

 (-4 + a)/3  =  -2-4 + a  =  -6a  =  -2 (-4 + b)/3  =  1-4 + b  =  3b  =  7

So, the third vertex is (-2, 7).

Problem 5 :

Master gave a triangular plate with vertices (5, 8), (2, 4) and (8, 3) and a stick to a student. He wants to balance the plate on the stick. Can you help the boy to locate that point which can balance the plate ?

Solution : The point which can balance the triangular plate is the centroid of the triangle.

Formula to find centroid of a triangle is

= [(x+ x+ x3)/3, (y+ y+ y3)/3]

x1  =  5, x2  =  2 and x3  =  8

y1  =  8, y2  =  4 and y3  =  3

=  [(5 + 2 + 8)/3, (8 + 4 + 3)/3]

=  (15/3, 15/3)

=  (5, 5)

So, the point which can balance the triangular plate is (5, 5). Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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