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Two perpendicular lines PQ and QR intersect at (1, -1). I...

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 is D

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)

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

\(y = -2x + 1 \implies y + 2x - 1 = 0\)

\(QR: 2x + y - 1 = 0\)