Find the Third Vertex of A δAbc If Two of Its Vertices Are B(-3,1) and C (0,-2) and Its Centroid is at the Origin - Mathematics

Find the third vertex of a  ΔABC if two of its vertices are B(-3,1)  and C (0,-2) and its centroid is at the origin

Solution

Two vertices of  ΔABC  are B(-3,1) and C (0,-2) .Let the third vertex be A (a, b).  Then, the coordinates of its centroid are

((-3+0+a)/3, (1-2+b)/3)

i.e ((-3+a)/3 , (-1+b)/3)

But it is given that the centroid is at the origin, that is G (0,0) Therefore

0= ((-3+a)/3,0=(-1+b)/3)

⇒ 0=-3+a,0=-1+b

⇒3= a,1=b

⇒ a=3, b=1

Therefore, the third vertex of  ΔABC  A(3,1).

Concept: Area of a Triangle
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 23