Question

T14114)
-
Two vertices of a AABC are A(2, 3) and B(1, -3) and its centroid is (3,0), then the co-ordinates of
its third vertex C is -
(A) (5,22
(B) (1,3)
(C) (6,0)
(D) (2, -3)
​

Answer 1

We are given the coordinates of the vertices of a triangle ABC where one of the vertices of the triangle are not given .The triangle's centroid's coordinates are given .Vertices are the three corners of a triangle .A centroid is the point which is equidistant from all the vertices of the triangle .

Let the vertex of C be ( x,y ) .

According to coordinate geometry :

A triangle A ( x₁,y₁ ) , B ( x₂,y₂ ) and C ( x₃,y₃ ) has the centroid D whose coordinate is ( x₁ + x₂ + x₃ )/3 , ( y₁ + y₂ + y₃ )/3 .

Comparing the above coordinate points with the given we have :

x₁ = 2

x₂ = 1

x₃ = x

Cx = 3

y₁ = 3

y₂ = -3

y₃ = y

Cy = 0

According to the formula of centroid we have :

( x₁ + x₂ + x₃ )/3 = Cx

⇒ ( 2 + 1 + x )/3= 3

⇒ ( 3 + x )/3 = 3

⇒ 3 + x = 3×3

⇒ 3 + x = 9

⇒ x = 9 - 3

⇒ x = 6

The y-coordinate will be :

( y₁ + y₂ + y₃ )/3 = Cy

⇒ ( 3 + (-3) + y )/3 = 0

⇒ ( y + 0 ) = 3×0

⇒ y = 0

Thus the third vertex will be ( x,y )

⇒ ( 6,0 )

Correct option is Option C .

Answer 2

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