AP EAMCET2014MathematicsStraight Lines

If the image of ( -7 5 , -6 5 ) in a line is (1,2) , then the equation of the line is

Options

A4 x+3 y=1
B3 x-y=0
C4 x-y=0
D3 x+4 y=1

Correct answer

D. 3 x+4 y=1

Step-by-step solution

The coordinate of mid-point of P Q is M ( - 7 5 +1 2 , - 6 5 +2 2 ) i.e., (- 1 5 , 2 5 ) Now, slope of P Q is m= 2+ 6 5 1+ 7 5 = 16 12 = 4 3 Since, the required line is perpendicular to P Q and passing through M (- 1 5 , 2 5 ) Equation of line is array rlrl & y- 2 5 =- & 1 4 / 3 (x+ 1 5 ) & 5 y-2 5 & =- 3 4 (5 x+1) 5 & 20 y-8 & =-15 x-3 & & 20 y+15 x & =5 or & & 4 y+3 x & =1 array

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