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coordinate geometry

coordinate geometry

by chanchal kumar -
Number of replies: 1
If G is the centroid and I the in-centre of the triangle, with vertices A(-36,7), B(20,7) and C(0,-8), then, find the value of GI.
In reply to chanchal kumar

Re: coordinate geometry

by rakhi mukherjee -
We know centroid G of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is 
(x1+x2+x3/3, y1+y2+y3/3) Therefore here co-ordinates of G is (-16/3, 2).
If a, b and c are the lengths of opposite sides of vertices (x1, y1), (x2, y2) and (x3, y3) respectively then in-centre will be given by
(ax1+bx2+cx3/a+b+c, ay1+by2+cy3/a+b+c).
Here a=25, b=39, c=56 and a+b+c = 120. Therefore co-ordinates of I = (-1, 0).
So, GI= (sqt of 205)/3.