JEE-Mains 2014 (18/30)

Geometry Level 3

Let P S PS be the median of the triangle with vertices P ( 2 , 2 ) , Q ( 6 , − 1 ) P(2,2),Q(6,-1) and R ( 7 , 3 ) R(7,3) . The equation of the line passing through ( 1 , − 1 ) (1,-1) and parallel to P S PS is:

2 x + 9 y + 7 = 0 2x+9y+7=0 2 x − 9 y − 11 = 0 2x-9y-11=0 4 x − 7 y − 11 = 0 4x-7y-11=0 4 x + 7 y + 3 = 0 4x+7y+3=0

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Midpoint of PQ,QR,PR is (4,0.5),(6.5,1),(4.5,2.5)respectively.Therefore, median is (5,4/3).Therefore, equation of the line passing through PS is 2x+9y=22(using point slope form) .Therefore, equation of the line passing through the point (1,-1) and parallel to PS is 2x+9y=-7 implies 2x+9y+7=0 (just substituting the value of x=1 and y=-1 because the lines are parallel).

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