Question

find the centroid of the traingle whose are (2,-4),(-3,-7),and (7,2) with steps​

Answer 1

Answer:

Given :-

• The triangle whose vertices are (2 , - 4) , (- 3 , - 7) , (7 , 2).

To Find :-

• What is the centroid of the triangle.

Formula Used :-

$\bigstar$ Centroid Formula :

$\mapsto \sf\boxed{\bold{\pink{Centroid\: G =\: \bigg\lgroup \dfrac{x_1 + x_2 + x_3}{3} , \dfrac{y_1 + y_2 + y_3}{3}\bigg\rgroup}}}$

where,

• x₁,x₂,x₃ = x co-ordinates of the vertices of the triangle
• y₁,y₂,y₃ = y co-ordinates of the vertices of the triangle

Solution :-

Given Points :

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

According to the question by using the formula we get,

$\leadsto \sf Centroid\: G(x,y) =\: \bigg\lgroup \dfrac{2 + (- 3) + 7}{3} , \dfrac{(- 4) + (- 7) + 2}{3}\bigg\rgroup$

$\leadsto \sf Centroid\: G(x,y) =\: \bigg\lgroup \dfrac{2 - 3 + 7}{3} , \dfrac{- 4 - 7 + 2}{3}\bigg\rgroup$

$\leadsto \sf Centroid\: G(x,y) =\: \bigg\lgroup\dfrac{\cancel{6}}{\cancel{3}} , \dfrac{- \cancel{9}}{\cancel{3}}\bigg\rgroup$

$\leadsto \sf Centroid\: G(x,y) =\: \bigg\lgroup\dfrac{2}{1} , \dfrac{- 3}{1}\bigg\rgroup$

$\leadsto \sf\bold{\red{Centroid\: G(x,y) =\: (2 , - 3)}}$

$\therefore$ The centroid of the triangle is 2 , - 3 .

Answer 2

Step-by-step explanation:

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