Question

find the centroid of the triangle whose vertices are (a,0),(0,a) and (a,a)​

Answer 1

Answer:

The coordinates of the centroid of the triangle are ( 2a / 3, 2a / 3 ).

Step-by-step-explanation:

Let the triangle be ABC.

The coordinates of the given points are

• A ( a, 0 ) ≡ ( x₁, y₁ )
• B ( 0, a ) ≡ ( x₂, y₂ )
• C ( a, a ) ≡ ( 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 = ( a + 0 + a ) / 3

⇒ x = ( a + a ) / 3

⇒ x = 2a / 3

Now,

y = ( y₁ + y₂ + y₃ ) / 3

⇒ y = ( 0 + a + a ) / 3

⇒ y = 2a / 3

∴ G ( x, y ) ≡ ( 2a / 3, 2a / 3 )

∴ The coordinates of the centroid of the triangle are ( 2a / 3, 2a / 3 ).