Home » Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ…

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ…

Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x – 2y + 4 = 0, find the equation of QR

  • A.
    x + 2y – 1= -0
  • B.
    2x + y – 3 = 0
  • C.
    x – 2y – 3 = 0
  • D.
    2x + y – 1 = 0
Correct Answer: Option D
Explanation

Line PQ : x – 2y + 4 = 0

2y = x + 4 (implies y = frac{x}{2} + 2 )

Slope = (frac{1}{2})

Slope of the perpendicular line QR: (frac{-1}{frac{1}{2}} = -2)

Line QR: (y = mx + b)

(y = -2x + b) 

Point of intersection: (1, -1)

(-1 = -2(1) + b implies b = -1 + 2 = 1)

(y = -2x + 1 implies y + 2x – 1 = 0)

(QR: 2x + y – 1 = 0)

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