Question

If the (2, 2) are coordinates of the centroid of a triangle whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.
1. 6
2. 8
3. -2
4. 4
5. None of these

Answer 1

Correct Answer - Option 2 : 8

Concept:

1. Centroid of the triangle:

If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are vertices of triangle then Centroid Formula is given by

\(x=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3}~\text{and}~y=\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3}~\)

Calculation:

Given vertices of a triangle are:

(x₁, y₁) = (0, 4)

(x₂, y₂) = (- 2, 0)

(x₃, y₃) = (p, 2)

Centroid = (x, y) = (2, 2)

Using the centroid formula,

\(x=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3}~\text{and}~y=\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3}\)

Equating the x- coordinates,

⇒ 2 = (0 - 2 + p)/3

⇒ (p - 2)/3 = 2

⇒ p - 2 = 2 × 3

⇒ p = 6 + 2

⇒ p = 8

Hence, the value of p = 8