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# A (3, 2) And B (−2, 1) Are Two Vertices of a Triangle Abc Whose Centroid G Has the Coordinates (5/3,-1/3)Find the Coordinates of the Third Vertex C Of the Triangle. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

A (3, 2) and B (−2, 1)  are two vertices of a triangle ABC whose centroid G has the coordinates (5/3,-1/3)Find the coordinates of the third vertex C of the triangle.

#### Solution

We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be(x,y).

The co-ordinates of other two vertices are A (3, 2) and C (−2, 1)

The co-ordinate of the centroid is(5/3,-1/3)

We know that the co-ordinates of the centroid of a triangle whose vertices are

(x_1,y_1),(x_2,y_2),(x_3,y_3)is

((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)

So, (5/3,-1/3)=((x+3-2)/3,(y+2+1)/3)

Compare individual terms on both the sides-

(x+1)/3=5/3

So,

x=4

Similarly

(y+3)/3=-1/3

So,

y=4

So the co-ordinates of third vertex (4,-4)

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Solution A (3, 2) And B (−2, 1) Are Two Vertices of a Triangle Abc Whose Centroid G Has the Coordinates (5/3,-1/3)Find the Coordinates of the Third Vertex C Of the Triangle. Concept: Concepts of Coordinate Geometry.
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