If the midpoint of the section of the straight line intercepted between the axes is (1, 1), then the equation of the line is

Question

If the midpoint of the section of the straight line intercepted between the axes is (1, 1), then the equation of the line is (A) 2x + y = 3 (B) 2x - y = 1 (C) x-y=0 (D) x+y=2

Tardigrade Admin · Accepted Answer

It is given that (1, 1) is the midpoint of line AB. ⇒ 1 = (a+0/2) , 1= (0+b/2) ⇒ a = 2 and b = 2 Equation of line AB is (x/2) + (y/2) = 1 ⇒ x + y = 2

Q. If the midpoint of the section of the straight line intercepted between the axes is $(1, 1)$ , then the equation of the line is

$2 x + y = 3$

$2 x - y = 1$

$x - y = 0$

$x + y = 2$

It is given that (1, 1) is the midpoint of line AB.
$\Rightarrow 1 = \frac{a + 0}{2}, 1 = \frac{0 + b}{2}$
$\Rightarrow a = 2$ and $b = 2$
Equation of line $A B$ is
$\frac{x}{2} + \frac{y}{2} = 1$
$\Rightarrow x + y = 2$

Q. If the midpoint of the section of the straight line intercepted between the axes is (1,1), then the equation of the line is

2x+y=3

2x−y=1

x−y=0

x+y=2