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If the image of the point P (2,1,0) in a line L is Q (0,-1,2) , and the line L passes through the points A (2,-2,0) and B (3, , ) , then the value of ²+ ² is equal to

Options

  1. A26
  2. B17
  3. C29 4
  4. D41 9

Correct answer

B. 17

Step-by-step solution

The line L is the line of reflection, so it must pass through the midpoint of the segment joining P and its image Q . Let M be the midpoint of P (2,1,0) and Q (0,-1,2) . M = ( 2+0 2 , 1-1 2 , 0+2 2 ) = (1,0,1) The line L passes through the known point A (2,-2,0) and the midpoint M (1,0,1) . The direction ratios of L are (2-1, -2-0, 0-1) = (1, -2, -1) . The symmetric equation of line L is: x-1 1 = y-0 -2 = z-1 -1 Since the point B (3, , ) lies on L , its coordinates must satisfy the line equation: 3-1 1 = -2 = -1 -1

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