First slide

Equation of line in Straight lines

Question

The length of portion of line $x + y - 2 = 0$ intercepted between the axes is

Easy

A

$2 \sqrt{2}$
B

$3 \sqrt{2}$
C

$\sqrt{2}$
D

1

Solution

The length of the portion of the line $\frac{x}{a} + \frac{y}{b} = 1$ intercepted between the axes is distance between the two points $(a, 0)$ and $(0, b)$
Rewrite the equation $x + y - 2 = 0$ as $\frac{x}{2} + \frac{y}{2} = 1$
Hence, the length of the portion of the line intercepted between the axes is distance between the points $(2, 0)$ and $(0, 2)$
$\begin{matrix} l = \sqrt{2^{2} + 2^{2}} \\ = \sqrt{8} \\ = 2 \sqrt{2} \end{matrix}$
Therefore, the length of the portion of the line $x + y - 2 = 0$ intercepted between the axes is $2 \sqrt{2} units$

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