Question

The origin 'O' is the centroid of ∆ABC in which A(–4, 3) B(3, k) and C(h, 5). Find h and k.

Answer 1

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Answer 2

Answer:

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}h=7andk=18

Step-by-step explanation: