Solution of missingVertex Question2

In this page solution of missingvertex question1 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 )

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, -9), B (-1,6) and let us take the third missing vertex be (a,b).

x₁ = -3          x₂ = 5             x₃ = a 

y₁ = -9          y₂ = -8           y₃ = b

(5/3 , -8/3) =  [(-3) + 5 + a ]/3 , [ (-9) + (-8) + b ]/3

(5/3 , -8/3) =  [-3 + 5 + a ]/3 , [ -9 - 8 + b ]/3

(5/3 , -8/3) =  [2 + a ]/3 , [ -17 + b ]/3

Equating x and y coordinates

[2 + a ]/3 = 5/3              [ -17 + b ]/3  = -8/3

2 + a = 5                          - 17 + b = -8

          a = 5 - 2                          b = -8 + 17

          a = 3                                  b = 9 

Therefore the third vertex is (3,9).

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 )



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