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Question Number 32834 by Rio Mike last updated on 03/Apr/18

f i n d t h e v a l u e o f k f o r w h i c h t h e

l e n g t h o f t h e l i n e s e g m e n t j o i n i n g

(\bar{k}, 2) a n d (- 1, 4) i s 2 \sqrt{2} u n i t s .

s h o w f u l l w o r k i n g \dots

Answered by MJS last updated on 03/Apr/18

\sqrt{{(k + 1)}^{2} + {(2 - 4)}^{2}} = 2 \sqrt{2}

\sqrt{k^{2} + 2 k + 5} = 2 \sqrt{2}

k^{2} + 2 k + 5 = 8

k^{2} + 2 k - 3 = 0

k = - 1 \pm \sqrt{1 + 3} = - 1 \pm 2

k_{1} = - 3

k_{2} = 1

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