Question

a) Find the
the centroid of the triangle
whose vertices (-5°,12) (8) 10) (6, -7)
are​

Answer 1

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Answer 2

Answer:

The coordinates of the centroid of the triangle are ( 3, 5 ).

Step-by-step-explanation:

Let the triangle be ABC.

The coordinates of the given points are

• A ( - 5, 12 ) ≡ ( x₁, y₁ )
• B ( 8, 10 ) ≡ ( x₂, y₂ )
• C ( 6, - 7 ) ≡ ( x₃, y₃ )

We have to find the coordinates of the centroid of the triangle.

Let the coordinates of centroid be G ( x, y ).

By centroid formula,

• x = ( x₁ + x₂ + x₃ ) / 3

• y = ( y₁ + y₂ + y₃ ) / 3

Now,

x = ( x₁ + x₂ + x₃ ) / 3

⇒ x = ( - 5 + 8 + 6 ) / 3

⇒ x = ( 3 + 6 ) / 3

⇒ x = 9 / 3

⇒ x = 3

Now,

y = ( y₁ + y₂ + y₃ ) / 3

⇒ y = ( 12 + 10 - 7 ) / 3

⇒ y = ( 12 + 3 ) / 3

⇒ y = 15 / 3

⇒ y = 5

∴ G ( x, y ) ≡ ( 3, 5 )

∴ The coordinates of the centroid of the triangle are ( 3, 5 ).