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If the image of point P (2,3) in a line L is Q (4,5) , then the image of point R (0,0) in the same line is:

Options

  1. A(2,2)
  2. B(4,5)
  3. C(3,4)
  4. D(7,7)

Correct answer

D. (7,7)

Step-by-step solution

Mid-point of P (2,3) and Q (4,5)=(3,4) Slope of PQ = 1 Slope of the line L =-1 Mid-point (3,4) lies on the line L . Equation of line L , y-4=-1(x-3) x+y-7=0 Let image of point R (0,0) be S (x₁, y₁ ) Mid-point of RS = ( x₁ 2 , y₁ 2 ) Mid-point ( x₁ 2 , y₁ 2 ) lies on the line (i) x₁+y₁=14 Slope of RS = y₁ x₁ Since RS line L aligned & y₁ x₁ (-1)=-1 &x₁=y₁ aligned From (ii) and (iii), x₁=y₁=7 Hence the image of R=(7,7)

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