A straight line through P (1, 2) is such that its intercept between the axes is bisected at P. Its equation is:

Question

A straight line through P (1, 2) is such that its intercept between the axes is bisected at P. Its equation is: (A)  x+y=-1  (B)  x+y=3  (C)  x+2y=5  (D)  2x+y=4

Tardigrade Admin · Accepted Answer

∵ P (1, 2) is midpoint of AB, therefore co-ordinate of A and B respectively (2, 0) and (0, 4) ∴ Equation of line AB is y-0=(4/-2)(x-4) ⇒ 2x+y=8

Q. A straight line through P (1, 2) is such that its intercept between the axes is bisected at P. Its equation is:

$x + y = - 1$

$x + y = 3$

$x + 2 y = 5$

$2 x + y = 4$

none of these

$∵$ P (1, 2) is midpoint of AB, therefore co-ordinate of A and B respectively (2, 0) and (0, 4)
$∴$ Equation of line AB is $y - 0 = \frac{4}{- 2} (x - 4)$ $\Rightarrow$ $2 x + y = 8$

Q. A straight line through P (1, 2) is such that its intercept between the axes is bisected at P. Its equation is:

x+y=−1

x+y=3

x+2y=5

2x+y=4