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COMEDK2020MathematicsStraight Lines

The coordinates of the foot of the perpendicular drawn from the point (3,4) on the line 2 x+y-7=0 is

Options

  1. A(1,5)
  2. B( 9 5 , 17 5 )
  3. C(1,-5)
  4. D(-5,1)

Correct answer

B. ( 9 5 , 17 5 )

Step-by-step solution

Let h, k be the coordinate of foot of perpendicular- Now, slope of line 2 x+y-7=0 is ( -2 1 ) , i.e. -2 . So, slope of perpendicular line. = -1 (-2) = 1 2 Equation of perpendicular line is given by aligned & y-4 &= 1 2 (x-3) & & 2 y-8 &=x-3 & x-2 y+5 &=0 aligned On solving 2 x+y-7=0 and x-2 y+5=0 , we get x= 9 5 and y= 17 5 So, (h, k)= ( 9 5 , 17 5 )

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