Question

If the distance between A(k, 3) and B(2, 3) is 5, then the value of k is

Answer 1

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Answer 2

SOLUTION

GIVEN

The distance between A(k, 3) and B(2, 3) is 5

TO DETERMINE

The value of m

FORMULA 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 the given points are A(k, 3) and B(2, 3)

Now the distance between A(k, 3) and B(2, 3) is 5

So by the given condition

$\sf{ \sqrt{ {(k - 2)}^{2} + {(3 - 3)}^{2} } = 5}$

$\sf{ \implies \sqrt{ {(k - 2)}^{2} + {(0)}^{2} } = 5}$

$\sf{ \implies \sqrt{ {(k - 2)}^{2} } = 5}$

$\sf{ \implies (k - 2) = \pm 5}$

Now k - 2 = 5 gives k = 7

k - 2 = - 5 gives k = - 3

FINAL ANSWER

Hence the required value of k = - 3 , 7

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