First slide

Equation of line in Straight lines

Question

A straight line through point $A (3, 4)$ is such that its intercept between the axes is bisected at $A .$ Its equation is

Moderate

A

$x + y = 7$
B

$3 x - 4 y + 7 = 0$
C

$4 x + 3 y = 24$
D

$3 x + 4 y = 25$

Solution

Let the equation of the line be $\frac{x}{a} + \frac{y}{b} = 1 .$ lt cuts the coordinates axes at $P (a, 0)$ and $Q (0, b) .$ It is given that $P Q$ is bisected at $A (3, 4) .$
$∴ \frac{a + 0}{2} = 3$ and $\frac{0 + b}{2} = 4 \Rightarrow a = 6, b = 8$ .
Hence, the equation of the line is $\frac{x}{6} + \frac{y}{8} = 1$ or, $4 x + 3 y = 24 .$

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