In this page solution of missingvertex question6 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 )

**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 )**

**Solution:**

**Centroid of a triangle = (x****₁+x****₂+x****₃)/3, (y****₁+y****₂+y****₃)/3**

let A,B and C be the vertices of triangle ABC. Here A (1, 10), B (-7,2) and let us take the third missing vertex be (a,b).

x₁ = 1 x₂ = -7 x₃ = a

y₁ = 10 y₂ = 2 y₃ = b

(-3, 19/3) = [ 1 + (-7) + a ]/3 , [ 10 + 2 + b ]/3

(-3 , 19/3) = [1 - 7 + a ]/3 , [ 10 + 2 + b ]/3

(-3, 19/3) = [-6 + a ]/3 , [12 + b ]/3

Equating x and y coordinates

[-6 + a ]/3 = -3 [ 12 + b ]/3 = 19/3

-6 + a = -3 x 3 12 + b = (19/3) x 3

-6 + a = -9 12 + b = 19

a = - 9 + 6 b = 19 - 12

a = -3 b = 7

Therefore the third vertex is (-3,7).

**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 )**