Question

A(h,-6), B(2,3) and C(-6,k) are the co-ordinates of vertices of a triangle whose centroid is G (1,5). Find h and k.

Answer 1

Given, A ≡ (h, -6) , B ≡(2,3) and C (-6, k) also centroid of given triangle ABC is G ≡(1,5) .

We know, if vertices of triangle are (x₁ , y₁) , (x₂, y₂) and (x₃, y₃)
Then, centroid of triangle is given by {(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 }

so, G ≡ (1, 5) ≡ { (h + 2 - 6)/3 , (-6 + 3 + k)/3 }
(h + 2 - 4)/3 = 1 ⇒ (h - 4)/3 = 1
⇒ h = 7

5 = (-6 + 3 + k)/3 ⇒ 5 = (-3 + k)/3
⇒15 = -3 + k
⇒k = 18

$\bf{h=7\:and\:k=18}$

Answer 2

Answer:Given, A ≡ (h, -6) , B ≡(2,3) and C (-6, k) also centroid of given triangle ABC is G ≡(1,5) .

We know, if vertices of triangle are (x₁ , y₁) , (x₂, y₂) and (x₃, y₃)

Then, centroid of triangle is given by {(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 }

so, G ≡ (1, 5) ≡ { (h + 2 - 6)/3 , (-6 + 3 + k)/3 }

(h + 2 - 4)/3 = 1 ⇒ (h - 4)/3 = 1

⇒ h = 7

5 = (-6 + 3 + k)/3 ⇒ 5 = (-3 + k)/3

⇒15 = -3 + k

⇒k = 18