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-1-

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