Question

If G is the centroid of triangle formed by A(2, 2), B(3, 4), C(7,3) find the slope of line AG.​

Answer 1

Answer:-

Given:-

G is the centroid of the triangle formed by the vertices A(2 , 2) , B(3 , 4) , C(7 , 3)

We know that,

Centroid of a triangle formed by the vertices (x₁ , y₁) , (x₂ , y₂) and (x₃ , y₃) is:

$\sf \:g(x \: ,\: y) = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: \: , \: \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)$

Let,

• x₁ = 2
• y₁ = 2
• x₂ = 3
• y₂ = 4
• x₃ = 7
• y₃ = 3

Putting the values we get,

$\implies \sf \: g(x \:, \: y) = \bigg( \dfrac{2 + 3 + 7}{3} \: \: , \: \: \dfrac{2 + 4 + 3}{3} \bigg) \\ \\ \\ \\ \implies \sf \: g(x \: , \: y) = \bigg( \dfrac{12}{3} \: \: , \: \: \dfrac{9}{3} \bigg) \\ \\ \\ \implies \boxed{\sf \: g(x \: , \: y) = ( 4 \: \: , \: \: 3 )}$

Now,

We know,

Slope of a line joining two points [ say (x₁ , y₁) , (x₂ , y₂) ] is;

⟹ m = (y₂ - y₁) / (x₂ - x₁)

We have to find the slope of AG.

Let,

• x₁ = 2
• y₁ = 2
• x₂ = 4
• y₂ = 3

Hence,

⟹ m = (3 - 2) / (4 - 2)

⟹ m = 1/2

∴ The slope of AG is 1/2.

Answer 2

Given

• G is the centroid of a triangle formed by A(2,2) B(3,4) C(7,3)

To find

• Slope of line AG

Solution

Centroid of triangle formed by 3 vertices :-

(x₁ , y₁) , (x₂ , y₂) and (x₃ , y₃)

• g (x , y) = (x₁ + x₂ + x₃ / 3 and y₁ + y₂ + y₃)

Here,

• x₁ = 2
• y₁ = 2
• x₂ = 3
• y₂ = 4
• x₃ = 7
• y₃ = 3

Substitute the values,

• g (x , y) = 2 + 3 + 7 / 3 , 2 + 4 + 3 / 3
• g (x , y) = 12 / 3 , 9 / 3
• g (x , y) = (4 , 3)

We know got the coordinates,

Using slope formula,

• y₂ - y₁ / x₂ - x₁

Here,

• x₁ = 2
• y₁ = 2
• x₂ = 4
• y₂ = 3

Substitute the values,

• (3 - 2) / (4 - 2)
• 1 / 2

Hence, the slope of line AG = (1 / 2)