Question

(2,3)(x,y)(3,-2) are vertices of a triangle. if the centroid is origin find x, y ?step by step explanation plz​

Answer 1

★Given:-

• (2,3)(x,y)(3,-2) are vertices of a triangle.
• Centroid is origin of triangle

★To find:-

• x and y

★Solution:-

We know:

★Point at origin is always (0,0)

Centroid formula:

★G(x,y) = (x₁+x₂+x₃/3, y₁+y₂+y₃/3)

We have,

• G(x,y) = (0,0)
• x₁ = 2 , y₁ = 3
• x₂ = x , y₂ = y
• x₃ = 3 , y₃ = -2

Substituting the values in the formula,

⇒(0,0) = (x₁+x₂+x₃/3, y₁+y₂+y₃/3)

⇒(0,0) = (2+x+3 /3 , 3+y-2 /3 )

⇒(0,0) = (5+x /3 , 1+y/3 )

Now,  

⇒5+x/3 = 0

⇒5 + x = 0

⇒x = -5

⇒1 + y /3 = 0

⇒1 + y = 0

⇒y = -1

Hence, (x,y) = (-5,-1)

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Know more:-

Centroid : The point of intersection of all the three medians.

Properties:

• The centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
• The centroid is the centre of the object.
• It is the centre of gravity.
• It always lie's inside the object.
• It is the point of concurrency of the medians.

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