Question

Find the centroid of the triangle whose vertices are ( -7 , 6) , ( 2, 5) , ( 8 , -2) *

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Answer 1

Answer:

Please find the image attached

Answer 2

Answer:

The coordinates of the centroid of the triangle are ( 1, 3 ).

Step-by-step-explanation:

Let the triangle be ABC.

The coordinates of the given points are

• A ( - 7, 6 ) ≡ ( x₁, y₁ )
• B ( 2, 5 ) ≡ ( x₂, y₂ )
• C ( 8, - 2 ) ≡ ( 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 = ( - 7 + 2 + 8 ) / 3

⇒ x = ( - 5 + 8 ) / 3

⇒ x = 3 / 3

⇒ x = 1

Now,

y = ( y₁ + y₂ + y₃ ) / 3

⇒ y = ( 6 + 5 - 2 ) / 3

⇒ y = ( 11 - 2 ) / 3

⇒ y = 9 / 3

⇒ y = 3

∴ G ( x, y ) ≡ ( 1, 3 )

∴ The coordinates of the centroid of the triangle are ( 1, 3 ).