Given the lines l_1 : x + y = 5 and l_2 : y = 4x and l_3 ; 4x + y − 1 =0 show that l_(2 ) is perpendicular to l_3 . find the point coordinates if x + 2y = 5 is colliner to l


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Question Number 39127 by Rio Mike last updated on 02/Jul/18

$G i v e n t h e l i n e s$ $l_{1} : x + y = 5 a n d l_{2} : y = 4 x$ $a n d l_{3}; 4 x + y - 1 = 0$ $s h o w t h a t l_{2} i s p e r p e n d i c u l a r$ $t o l_{3} .$ $f i n d t h e p o i n t c o o r d i n a t e s$ $i f x + 2 y = 5 i s c o l l i n e r t o l_{1}$
Commented by mondodotto@gmail.com last updated on 03/Jul/18

$t w o l i n e s a r e s a i d t o b e p e r p i n d i c u l a r i f p r o d u c t o f t h e i r$ $g r a d i e n t e q u a l s (- 1)$ $f r o m l_{2} g r a d i e n t i s 4 a n d$ $l_{3} g r a d i e n t i s (- 4) t h e n$ $p r o d u c t o f t h e s e g r a d i e n t i s n o t (- 1)$ $∴ l_{2} a n d l_{3} n o t p e r p e n d i c u l a r l i n e s$
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