Find the value of a, if distance between $A (- 9, 8)$ and $B (- 5, a)$ is $5$ units.

5, 11

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4, 10

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5, 10

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4, 11

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Solution

The correct option is B $5, 11$
$A B = \sqrt{(- 9 + 5)^{2} + (8 - a)^{2}}$
$25 = 16 + (8 - a)^{2}$ ,
$(8 - a)^{2} = 9$
$(8 - a)^{2} = (3)^{2}$
$8 - a = \pm 3$
$a = 8 - 3 = 5$ or
$a = 8 + 3 = 11$
So, option A is correct.

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