Lines represented by x-y=0 and x+y=0 are perpendicular to each other.

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Solution

Dear Student,

If the question is to prove that "Lines represented by x-y=0 and x+y=0 are perpendicular to each other."
$T h e t w o e q u a t i o n s o f l i n e s a r e y - x = 0 a n d y + x = 0 \Rightarrow y = x a n d y = - x c o m p a r i s n g t h e s e w i t h s l o p e e q u a t i o n o f l i n e y = m x + c w e g e t c = 0 a n d m i . e t h e s l o p e o f l i n e f o r y = x, m_{1} = 1 a n d y = - x, m_{2} = - 1 w e k n o w t h a t f o r t w o l i n e s t o b e p e r p e n d i c u l a r t h e p r o d u c t o f s l o p e s = - 1 f o r t h e g i v e n l i n e s m_{1} \times m_{2} = 1 \times (- 1) m_{1} \times m_{2} = - 1 H e n c e t h e t w o l i n e s y = x a n d y = - x a r e p e r p e n d i c u l a r .$
Regards,

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