Solution of missingVertex Question4

In this page solution of missingvertex question4 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 )

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 (3, 1), B (2,2) and let us take the third missing vertex be (a,b).

x₁ = 3           x₂ = 2             x₃ = a 

y₁ = 1           y₂ = 2             y₃ = b

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

(7/3 , 1) =  [5 + a ]/3 , [ 3 + b ]/3

(7/3 , 1) =  [5 + a ]/3 , [3 + b ]/3

Equating x and y coordinates

[5 + a ]/3 = 7/3              [ 3 + b ]/3  = 1

5 + a = (7/3) x 3                      3 + b = 1 x 3

5 + a = 7                                 3 + b = 3

         a = 7 - 5                          b = 3 - 3

          a = 2                              b = 0 

Therefore the third vertex is (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 )



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