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Distance Formula

What points o...

Question

What points on the x-axis are at a distance of 5 units from the point (5, - 4) ?

(2, 0) and (8, 0)

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(2, 1), (8, 1)

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(-2, 0) (-8, 0)

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None of these

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Solution

The correct option is B (2, 0) and (8, 0)
$L e t t h e p o i n t b e A = (x_{1}, y_{1}) = (p, 0) [s i n c e i t i s o n t h e X - a x i s] & a t a d i s t a n c e o f d = 5 u n i t s f r o m t h e p o i n t B = (x_{2}, y_{2}) = (5, - 4) . N o w t h e d i s t a n c e b e t w e e n t w o p o i n t s (x_{1}, y_{1}) a n d (x_{2}, y_{2}) i s d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} ∴ \sqrt{{(5 - p)}^{2} + {(- 4 - 0)}^{2}} = 5 ⟹ p^{2} - 10 p + 16 = 0 ⟹ (p - 8) (p - 2) = 0 ∴ p = 8 o r 2 S o t h e p o i n t s a r e (8, 0) & (2, 0) A n s - O p t i o n A$

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