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
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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)