Solution of missingVertex Question3

In this page solution of missingvertex question3 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 )

Question 2 :

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

Question 3 :

Find the missing vertex of triangle whose two vertices are (4,5) (4,2) and its centroid is (2 , 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 (4, 5), B (4,2) and let us take the third missing vertex be (a,b).

x₁ = 4 x₂ = 4 x₃ = a

y₁ = 5 y₂ = 2 y₃ = b

(2, 3) = [ 4 + 4 + a ]/3 , [ 5 + 2 + b ]/3

(2 , 3) = [8 + a ]/3 , [ 7 + b ]/3

(2 , 3) = [8 + a ]/3 , [7 + b ]/3

Equating x and y coordinates

[8 + a ]/3 = 2 [ 7 + b ]/3 = 3

8 + a = 2 x 3 7 + b = 3 x 3

8 + a = 6 7 + b = 9

a = 6 - 8 b = 9 - 7

a = -2 b = 2

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

Question 4 :

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

Question 5 :

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

Question 6 :

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

Question 7 :

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

Question 8 :

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