A triangle ABC is formed by three lines x+y+2=0,x-2y+5=0 and 7x+y-10=0. P is a point inside the triangle ABC such that areas of the triangles PAB,PBC and PCA are equal. If the co-ordinates of the point P are (a,b) and the area of the triangle ABC is ‘g’, then find (a+b+g).

[P.S. The answer to this question is supposed to be 15.Just tell me how.]

Question

Harsh Hardik · Answer

To take out the coordinates of A,B and C use the point of intersection of lines so, coordinates of A come to be x+y=-2 and x-2y=-5 then by using elimination method the coordinates of A come to be (-3,1). Similarly of B (2,-4) and C (1,3). Area of triangle ABC g=1/2[-3(-4-3)+2(3-1)+1(1+4)] and g comes out to be 15 by using area of triangle. Now,P is a centroid of the triangle ABC as it divides the triangle into 3 equal areas. so P(a,b) here x=a and y=b coordinate. Now, a=x1+x2+x3/3 a=-3+2+1/3=0 similarly of b = 1-4+3/3 = 0 so, a+b+g=0+0+15=15 hope it is clear!!! Regards Harsh Hardik Student of fiitjee

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