Question

If x is a negative integer such that distance between (x, 2) and (4, – 6) is 10 units, then x equals
(a) 10 (b) 12 (c) – 10 (d) – 2

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If x is a negative integer such that distance between (x, 2) and (4, – 6) is 10 units, then x equals

(a) 10

(b) 12

(c) – 10

(d) – 2

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

EVALUATION

Here it is given that distance between (x, 2) and (4, – 6) is 10 units

So by the given condition

$\displaystyle \sf{ \sqrt{ {(x - 4)}^{2} + {(2 + 6)}^{2} } = 10 }$

$\displaystyle \sf{ \implies {(x - 4)}^{2} + {(8)}^{2} } = {10}^{2}$

$\displaystyle \sf \implies {(x - 4)}^{2} + 64 = 100$

$\displaystyle \sf \implies {(x - 4)}^{2} = 36$

$\displaystyle \sf \implies {(x - 4)}^{} = \pm 6$

x - 4 = 6 gives x = 10

x - 4 = - 6 gives x = - 2

Since x is a negative integer

So x = - 2

FINAL ANSWER

Hence the correct option is (d) – 2

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