find the value of k for which the length of the line segment joining (k^� ,2) and (−1,4) is 2(√2) units. show full working...


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

$f i n d t h e v a l u e o f k f o r w h i c h t h e$ $l e n g t h o f t h e l i n e s e g m e n t j o i n i n g$ $(\bar{k}, 2) a n d (- 1, 4) i s 2 \sqrt{2} u n i t s .$ $s h o w f u l l w o r k i n g . . .$
	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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