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COMEDK2018MathematicsStraight Lines

If the line through A=(4,-5) is inelined at an angle 45^ with the positive direction of the X -axis, then the coordinates of the two points on opposite sides of A at a distance of 3 2 units are

Options

  1. A(7,2),(1,8)
  2. B(7,2),(1,-8)
  3. C(7,-2),(1,-8)
  4. D(7,2),(-1,8)

Correct answer

C. (7,-2),(1,-8)

Step-by-step solution

If the line is inclined at angle 45^ with the positive direction of the X -axis i.e. the points are situated at angle =45^ from X -axis at a distance r=3 2 from point (4,-5) . The two points can be given by (x₀ r , y r ) The points are aligned (4& .+3 2 45^ ,-5+3 2 45^ ) &= (4+3 2 1 2 ,-5+3 2 1 2 )=(7,-2) aligned aligned & and (4-3 2 45^ ,-5-3 2 45^ ) &= (4-3 2 1 2 ,-5-3 2 1 2 )=(1,-8) aligned Thus, the points are (1,-8) and (7,-2) .

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