Find the distance between the following pairs of points. $(a, b), (- a, - b)$

4 (a^{2} + b^{2})^{\frac{1}{2}}

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2 \sqrt{a^{2} + b^{2}}

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8 (a^{2} + b^{2})^{\frac{1}{2}}

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3 (a^{2} + b^{2})^{\frac{1}{2}}

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Solution

The correct option is D $2 \sqrt{a^{2} + b^{2}}$
Let $A (a, b) \equiv (x_{1}, y_{1})$ and $B (- a, - b) \equiv (x_{2}, y_{2})$ be the points of a straight line.

$A B = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

$A B = \sqrt{{(- a - a)}^{2} + {(- b - b)}^{2}}$

$= \sqrt{{(- 2 a)}^{2} + {(- 2 b)}^{2}}$

$= \sqrt{4 a^{2} + 4 b^{2}} = 2 \sqrt{a^{2} + b^{2}}$ units.

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