Solution of missingVertex Question8

In this page solution of missingvertex question8 we are going to see he detailed solution of the first question.

Question 1 :

Find the missing vertex of triangle whose two vertices are (-3,-9) (-1,6) and its centroid is (-1/3 , 2 )



(A) (1 , -2)
(B) (3 , 9)
(C) (1 , -5)




Question 2 :

Find the missing vertex of triangle whose two vertices are (-3,-9) (5,-8) and its centroid is (5/3 , -8/3 )



(A) (1 , -2)
(B) (3 , 9)
(C) (1 , -5)




Question 3 :

Find the missing vertex of triangle whose two vertices are (4,5) (4,2) and its centroid is (2 , 3 )



(A) (-2 , 2)
(B) (3 , 6)
(C) (1 , 2)




Question 4 :

Find the missing vertex of triangle whose two vertices are (3,1) (2,2) and its centroid is (7/3 , 1 )



(A) (-2 , 1)
(B) (2 , 6)
(C) (2 , 0)




Question 5 :

Find the missing vertex of triangle whose two vertices are (3,1) (0,4) and its centroid is (0 , 2 )



(A) (-2 , 0)
(B) (-3 , 1)
(C) (-1 , 2)




Question 6 :

Find the missing vertex of triangle whose two vertices are (1,10) (-7,2) and its centroid is (-3 , 19/3 )



(A) (-3 , 7)
(B) (3 , 1)
(C) (1 , 0)




Question 7 :

Find the missing vertex of triangle whose two vertices are (-1,-3) (2,1) and its centroid is (1 , -2 )



(A) (-3 , 4)
(B) (2 , -4)
(C) (1 , 4)




Question 8 :

Find the missing vertex of triangle whose two vertices are (1,1) (2,3) and its centroid is (-1/3 , 2 )

Solution:

Centroid of a triangle = (x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3

let A,B and C be the vertices of triangle ABC. Here A (1, 1), B (2,3) and let us take the third missing vertex be (a,b).

x₁ = 1            x₂ = 2             x₃ = a 

y₁ = 1            y₂ = 3             y₃ = b

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

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

(-1/3, 2) =  [3 + a ]/3 , [4 + b ]/3

Equating x and y coordinates

[3 + a ]/3 = 1/3                   [ 4 + b ]/3  = 2

3 + a = (1/3) x 3                         4 + b = 2 x 3

3 + a = 1                              4 + b = 6

         a = 1 - 3                         b = 6 - 4

          a = -2                              b = 2 

Therefore the third vertex is (-2,2).