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KCET2007MathematicsThree Dimensional Geometry

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

Correct answer

A. ( 9 5 , 17 5 )

Step-by-step solution

We know that foot of the perpendicular (h, k) from (x₁, y₁ ) to the line a x+b y+c=0 is given by h-x₁ a = k-y₁ b = - (a x₁+b y₁+c ) a²+b² Here, point (x₁, y₁ )=(3,4) and a x+b y+c=2 x+y-7=0 a=2, b=1, c=-7 then, from Eq. (i) h-3 2 = k-4 1 = -(2 3+1 4-7) 2²+1² h-3 2 = k-4 1 = -3 5 h= +9 5 and k= 17 5

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