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 )**

**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 )**

**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 )**

**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, 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).