If the distance between the points (3, –5) and (x, –5) is 15 units, then the values of x are

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Solution

Q.
If the distance between the points (3, –5) and (x, –5) is 15 units, then the values of x are :

1 12, –18

2 –12, 18

3 18, 5

4 –9, –12

Ans.
(2)

$Here, (15)^{2} = {(3 - x)}^{2} + {(- 5 + 5)}^{2}$

$\Rightarrow 225 = 9 - 6 x + x^{2} \Rightarrow x^{2} - 6 x - 216 = 0$

$\Rightarrow x^{2} - 18 x + 12 x - 216 = 0 \Rightarrow x (x - 18) + 12 (x - 18) = 0$

$\Rightarrow (x - 18) (x + 12) = 0 \Rightarrow x = - 12, 18$

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