Question

The point A(b, a) lies on the straight line 2x + 3y = 13 and the point B(a, b) lies on the straight line -x + 4y = 5, then the equation of line AB is ______

Options

• x - y = 5

• x + y = 5

• x + y = -5

• x - y = -5

Answer 1

The point A(b, a) lies on the straight line 2x + 3y = 13 and the point B(a, b) lies on the straight line -x + 4y = 5, then the equation of line AB is x + y = 5.

Explanation:

Point A(b, a) is on 2x + 3y = 13

So, 2b + 3a = 13 ........(i)

Point B(a, b) is on -x + 4y = 5

So, 4b - a = 5 .............(ii)

By solving (i) and (ii), we get

a = 3, b = 2

Now, equation of AB is

`y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)`

⇒ `y - 3 = (2 - 3)/(3 - 2)(x - 2)`

⇒ y - 2 = -(x - 3)

⇒ x + y = 5