Correct Answer – Option 2 : y + 2x – 3 = 0

Concept:

The general equation of a line is y = mx + c 

where m is the slope and c is any constant

• Slope of parallel lines is equal.
• Slope of the perpendicular line have their product = -1

Equation of a line with slope m and passing through (x1, y1)

(y – y1) = m (x – x1)

Equation of a line passing through (x1, y1) and (x2, y2) is:

\(\rm {y-y_1\over x-x_1}={y_2-y_1\over x_2-x_1}\)

Calculation:

Given lines are:

2x – y = 1   …(i)

x + 2y = 3  …(ii)

Adding 2 × (i) to (ii)

⇒ 5x = 5

⇒ x = 1

Putting value of x in (i)

2(1) – y = 1

⇒ y = 1

The intersection is (1, 1)

So line has the slope -2 and passes through (1, 1)

∴ Equation of the perpendicular line is

(y – y1) = m (x – x1)

⇒ y – 1 = -2 (x – 1)

⇒ y + 2x – 3 = 0