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AP EAMCET202422 May 2024Evening ShiftMathematicsStraight LinesActual

If the reflection of a point A (2,3) in X -axis is B ; reflection of B in the line x+y=0 is C and the reflection of C in x-y=0 is D then the point of intersection of the lines CD , AB is

Options

  1. A(3,-2)
  2. B(0,1)
  3. C(4,-3)
  4. D(2,-1)

Correct answer

D. (2,-1)

Step-by-step solution

We know, reflection about X -axis of (x, y) is (x,-y) So, co-ordinates of B are (2,-3) We know, reflection about line x+y=0 of (x, y) is (-y,-x) So, co-ordinates of C are (3,-2) We know, reflection about x-y=0 of (x, y) is (y, x) So, co-ordinates of D are (-2,3) Equation of AB is, y-3= -3-3 2-2 (x-2) x=2 Equation of CD is, y+2= 3+2 -2-3 (x-3) x+y=1 Point of intersection of line AB and CD is (2,-1)

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