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)