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I 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.

I 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.

Grade:11

2 Answers

TULJAVAMSHIKIRAN BUYAKAR
16 Points
13 years ago

answer is 4.7

AJIT AskiitiansExpert-IITD
68 Points
13 years ago

Dear Chanchal ,

 (x_I,y_I)=((ax_1+bx_2+cx_3)/(a+b+c),(ay_1+by_2+cy_3)/(a+b+c)).    is  the formulae for the incentre of triangle  and the centroid of a triangle is given by (x2 , y2)  =   (x1+x2+x3/3 .y1+y2+y3/3)

so , G = (-36+20+0/3 ,  7+7+(-8)/3) ;  G = (-16/3 , 2)

a = BC = 25 , b =AC = 39 , c =AB  = 56

therefore ,

I = [25*(-36)+39*(20)+56*(0)/(25+39+56),  25*(7)+39*(7)+56*(-8)/(25+39+56) ]

I =[-1 , 0]

therfore ,

IG  =  4.77 (use simply heroes formulae)

GOOD LUCK !!!

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