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 ______

पर्याय

• 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

${\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)}$

⇒ ${\displaystyle y-3=\frac{2-3}{3-2}(x-2)}$

⇒ y - 2 = -(x - 3)

⇒ x + y = 5