Question

D
Centroid of a triangle formed by (7. p). (9,-6) and (9, 10) is (6,3), then
value of (p + q) is:
b
7​

Answer 1

Question:

Centroid of a triangle formed by ( 7, p ), ( q, - 6. ) and ( 9, 10 ) is ( 6, 3 ), then value of ( p + q ) is:

Answer:

The value of ( p + q ) is 7.

Step-by-step-explanation:

Let the triangle be ABC with centroid G.

The coordinates of the given points are

• A ( 7, p ) ≡ ( x₁, y₁ )
• B ( q, - 6 ) ≡ ( x₂, y₂ )
• C ( 9, 10 ) ≡ ( x₃, y₃ )

• G ( 6, 3 ) ≡ ( x, y )

We have to find the value of ( p + q ).

By centroid formula,

• x = ( x₁ + x₂ + x₃ ) / 3

• y = ( y₁ + y₂ + y₃ ) / 3

Now,

x = ( x₁ + x₂ + x₃ ) / 3

⇒ 6 = ( 7 + q + 9 ) / 3

⇒ 6 * 3 = q + 9 + 7

⇒ 18 = q + 16

⇒ q = 18 - 16

⇒ q = 2

Now,

y = ( y₁ + y₂ + y₃ ) / 3

⇒ 3 = ( p - 6 + 10 ) / 3

⇒ 3 * 3 = p + 4

⇒ 9 = p + 4

⇒ p = 9 - 4

⇒ p = 5

∴ ( p, q ) = ( 5, 2 )

Now,

p + q = 5 + 2

⇒ p + q = 7

∴ The value of ( p + q ) is 7.