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COMEDK2012MathematicsStraight Lines

The image of the point (2,4) on the line x+y-10=0 is

Options

  1. A(4,8)
  2. B(6,5)
  3. C(6,8)
  4. D(0,10)

Correct answer

C. (6,8)

Step-by-step solution

Let the image of point (2,4)=(h, k) , then h-x₁ a = k-y₁ b = -2 (a x₁+b y₁+c ) a²+b² h-2 1 = k-4 1 = -2(2+4-10) 1²+1² h-2 1 = k-4 1 = -2(-4) 2 h-2 1 = k-4 1 =4h-2=4 and k-4=4h=6 and k=8 So, (h, k)=(6,8)

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