Find the distance between the $x$ -intercept and $y -$ intercept of the line $\frac{1}{2} x - 4 y = 8$ .

5

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8

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\sqrt{256}

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\sqrt{260}

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Solution

The correct option is B $\sqrt{260}$
Given equation is $\frac{1}{2} x - 4 y = 8$
Writing in intercept form, we get
$\frac{x}{16} + \frac{y}{- 2} = 1$

Hence, $x_{i n t e r c e p t} = 16$ and $y_{i n t e r c e p t} = - 2$ .

Thus, distance $= \sqrt{x_{i n t e r c e p t}^{2} + y_{i n t e r c e p t} 2} = \sqrt{16^{2} + (- 2)^{2}} = \sqrt{260}$

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