Correct Answer – Option 1 : (1, 5)

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 are equal.
• Slope of 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:

The line has the slope -1 and passes through (2, 4)

∴ Equation of the perpendicular line is

(y – y1) = m (x – x1)

⇒ y – 4 = -1 (x – 2)

⇒ y  = –x + 6   …(i)

Slope(m1) = -1 and c1 = 6

Now for the slope of perpendicular line (m2)

m1 × m2 = -1

⇒ -1 × m2 = -1 

⇒ m2 = 1

Perpendicular line has the slope 1 and passes through (-1, 3)

∴ Equation of the perpendicular line is

(y – y1) = m (x – x1)

⇒ y – 3 = 1 (x – (-1))

⇒ y = x + 4   …(ii)

Adding (i) and (ii)

⇒ 2y = 10

⇒ y = 5

Putting y in equation (ii)

5 = x + 4

⇒ x = 1

∴ The point of intersection is (1, 5)