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-non

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}