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=(0, 0)

Exa7-:-If (4, k) is the centroid of the triangle with vertices (p, 4), (5, -2) and
(-8, 3), find the values of p and k.
Soln:Coordinates of the centroid D(x, y) of the triangle with vertices A(x 1 , y 1 ), B(x 2 , y 2 ) and
C(x 3 , y 3 ) can be found using the formula

,

4 = (p + 5 - 8)/3 = (p - 3)/3
12 = p - 3
Therefore, p = 15
Similarly,
k = (4 - 2 + 3)/3 = 5/3
Therefore, co-ordinates of the centroid D = (6, 5/3) and the three vertices are:
(15, 6), (5, -2), (-8, 3)
Exa:8-Find the third vertex of a triangle whose two vertices are (1, 3) and
(4, -5) and centroid is (7, 2).

Let the third vertex be (x, y)
Centroid of a triangle with vertices (x 1, y 1 ), (x 2, y 2 ), (x 3, y 3 ) is given by

Substituting values

x + 1 + 4 = 21 and y + 3 - 5 = 6

x = 21-4-1 and y = 6 + 5 - 3
Therefore, x = 16 and y = 8
Therefore, the third vertex is (16, 8)
Exa:9- In what ratio is the line segment joining (-3, -1) and (-8, -9) divided by the

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