Question

The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G 1,1/2

   Find the coordinates of the third vertex C of the ΔABC.

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Answer 1

Key Point:-

Let, (a,b);(c,d) and (e,f) are vertices of ∆ABC

Then, Centroid is given by

((a+c+e)/3 , (b+d+f)/3)

Let, third vertex of triangle be (x,y)

and, Centroid = ((2+2+x)/3 , (3+1+y)/3/

or, (1,1/2) = ((4+x)/3 , (4+y)/3)

on comparing

(4+x)/3 = 1

or, 4+x = 3 or, x = -1

and (4+y)/3 = 1/2

or, 8+2y = 3

or, 2y = -5

or, y = -5/2

Hence, third vertex is (-1,-5/2)