Question

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.

Answer 1

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).