If the coordinate of the points A and B be (3,3) and (7,6) then the length of the portion of the line AB intercepted between the axes is (a) (5/4) (b) ((√(10))/4) (c) ((√(13))/3) (d) none


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Question Number 40847 by LXZ last updated on 28/Jul/18

$I f t h e c o o r d i n a t e o f t h e p o i n t s A$ $a n d B b e (3, 3) a n d (7, 6) t h e n t h e$ $l e n g t h o f t h e p o r t i o n o f t h e l i n e$ $A B i n t e r c e p t e d b e t w e e n t h e a x e s i s$ $(a) \frac{5}{4} (b) \frac{\sqrt{10}}{4} (c) \frac{\sqrt{13}}{3} (d) n o n e$
	Answered by tanmay.chaudhury50@gmail.com last updated on 28/Jul/18

	$e q n o f s t l i n e i s y - 3 = \frac{6 - 3}{7 - 3} (x - 3)$ $4 (y - 3) = 3 (x - 3)$ $4 y - 12 = 3 x - 9$ $- 3 x + 4 y = 12 - 9$ $- 3 x + 4 y = 3$ $\frac{x}{- 1} + \frac{y}{\frac{3}{4}} = 1$ $s o t h e l i n e c u t s x a x i s a t (- 1, 0) y a x i s a t (0, \frac{3}{4})$ $s o l e n g t h o f i n t e r c e p t b e t w e e n a x e s$ $\sqrt{{(0 + 1)}^{2} + {(\frac{3}{4} - 0)}^{2}}$ $= \sqrt{1 + \frac{9}{16}} = \frac{5}{4}$
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