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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
9.16 Centroid of a Triangle

To find the centroid of a triangle whose vertices are given

Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle ABC. Let AD be the median bisecting the base.
Then D = {(x2 + x3)/2, (y2 + y3)/2}
Now the point G on AD, which divides it internally in the ratio 2:1, is the centroid. If (x,y) are the coordinates of G, then
x = 2x(x2+x3)/2 + (1 x x1)/2+1 = (x1+x2+x3)/3
y = 2x(y2+y3)/2 + (1 x y1)/(2+1) = (y1+y2+y3)/3
Hence, the coordinates of the centroid are given by
x = (x1+x2+x3)/3, y = (y1+y2+y3)/3.

Directions: Solve the following.
Q 1: The coordnates of the vertices of the triangle are (4, -3), (-5,2) and (x,y). If the centroid of the triangle is at the origin, what is the value of x and y.
0
(1,1)
(0,1)
1

Q 2: Find the centroid of the triangle whose angular points are (3, -5), (-7, 4) and (10, -2) respectively.
(2, -1)
(-2, 1)
(-2, -1)
(2, 1)

Q 3: Origin is the centroid of the triangle, whose two vertices are (5, -1), (-2,3).Find the third vertex.
(3, 2)
(3,-2)
(-3, -2)

Q 4: Find the centroid of the triangle formed by the lines 3x-y-11 = 0, 7y+x-11 = 0, 2x+3y = 0
(-4/3, -1/3)
(-4/3, 1/3)
(4/3, 1/3)

Q 5: If (2,4) is the centroid of the triangle two of whose vertices are (7,1) and (2,7). Find the remaining vertex.
(3,-4)
(-3,-4)
(-3,4)
(3,4)

Q 6: Find the centroid of the triangle whose angular points are (-1,0), (5, -2) and (8, -2)
(-4,0)
(0, 4)
(4, 0)
(0, -4)

Q 7: The vertices of a triangle are (1,2), (h, -3) and (-4, k). FInd the values of h and k if the centroid of the triangle be at the point (5, -1).
(8, 2)
(-18, -2)
(2, 18)
(18, -2)

Q 8: Find the length of the median AD of a triangle whose vertices are A(4,4), B(3,-2) and C(-3,16).
10
5
7
3

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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