4: IIT LEVEL SOLVED i

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This is an advanced question where the lines forming the triangles are NOT given. Rather, their perpendicular bisectors are given. And it so happens that if you draw out accurately the geometry opens out in front of you and the rest is a cinch. 


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This is a slightly different method for solving the earlier problem. In the previous solution we used geometry extensively. Here we have simply used a formula for distance from a point to the line. 

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In the question, the examiner has used a cryptic way to delineate the three vertices of the triangle. the three vertices have been given distinct names for their coordinates but have been expressed in short by xi & yi as shown. 

Since a and b remains the same for the line given, the denominator of the perpendicular distances from the three distinct points remain the same and that has been taken common and we have jumped a few steps to get to the solution. 

If you see the abbreviated way we have dealt with algebra here, you will progress far because such accurately accelerated methods for solving algebra is highly required for you to excel in mathematics at a higher level.