In this page solution of missingvertex question5 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 )**

**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 (3, 1), B (0,4) and let us take the third missing vertex be (a,b).

x₁ = 3 x₂ = 0 x₃ = a

y₁ = 1 y₂ = 4 y₃ = b

(0, 2) = [ 3 + 0 + a ]/3 , [ 1 + 4 + b ]/3

(0 , 2) = [3 + a ]/3 , [ 5 + b ]/3

(0, 2) = [3 + a ]/3 , [5 + b ]/3

Equating x and y coordinates

[3 + a ]/3 = 0 [ 5 + b ]/3 = 2

3 + a = 0 x 3 5 + b = 2 x 3

3 + a = 0 5 + b = 6

a = 0 - 3 b = 6 - 5

a = -3 b = 1

Therefore the third vertex is (-3,1).

**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 )**