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AP EAMCET202120 Aug 2021Evening ShiftMathematicsStraight LinesActual

If A ( 1 , 3 ) and C ( 7 , 5 ) are two opposite vertices of a square, then find the equation of a side passing through A .

Options

  1. Ax = y
  2. Bx - 2   y + 1 = 0
  3. Cx - 3   y + 8 = 0
  4. D2   x - y + 1 = 0

Correct answer

D. 2   x - y + 1 = 0

Step-by-step solution

Let A B C D be a square where A ≡ 1 , 3 & C ≡ 7 , 5 . ∴   Equation of diagonal A C is y - 5 3 - 5 = x - 7 1 - 7 ⇒   3 y - 15 = x - 7 ⇒   3 y - x - 8 = 0     . . . 1 ∴   Slope of A C is 1 3 Suppose slope of A B   is m . ∵   Diagonal makes 45 °   with the side. ∴   m - 1 3 1 + 1 3 × m = tan 45 ° ⇒   3 m - 1 3 + m = 1 ⇒   3 m - 1 3 + m 2 = 1 ⇒   9 m 2 - 6 m + 1 = 9 + m 2 + 6

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