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One of the diagonals of a square lies along the line 3x - 4y + 10 = 0 . If one of the vertices of the square is (3, 1) , then the area of the square is

Options

  1. A18
  2. B9
  3. C9 2
  4. D12

Correct answer

A. 18

Step-by-step solution

Let the given vertex be A(3, 1) and the given diagonal lie on the line L: 3x - 4y + 10 = 0 . The perpendicular distance d from the vertex A to the diagonal L is given by d = |3(3) - 4(1) + 10| 3^2 + (-4)^2 = |9 - 4 + 10| 5 = 15 5 = 3 In a square, the diagonals bisect each other at right angles. Thus, the perpendicular distance from any vertex to the opposite diagonal is exactly half the length of the diagonal. Let the length of the diagonal be D . Then D 2 = 3 D = 6 . The area of a square in terms of its diagonal D

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