Prove that through a given point , we can draw only one perpendicular to a given line .

Asked by SIDDHARTH SHARMA | 13th Sep, 2014, 11:47: PM

Expert Answer:

W e space n e e d space t o space p r o v e space t h a t space t h r o u g h space a space g i v e n space p o i n t comma space o n l y space o n e space p e r p e n d i c u l a r space t o space a space g i v e n space l i n e. L e t space u s space p r o v e space t h i s space b y space t h e space m e t h o d space o f space c o n t r a d i c t i o n. A s s u m e space t h a t space t h r o u g h space a space g i v e n space p o i n t space t w o space p e r p e n d i c u l a r space l i n e s space c a n space b e space d r a w space t o space a space g i v e n space l i n e. L e t space l space b e space t h e space g i v e n space l i n e space a n d space l e t space P space b e space t h e space g i v e n space p o i n t. L e t space m space a n d space n space t w o space p e r p e n d i c u l a r space l i n e s space t o space l rightwards double arrow m perpendicular l space a n d space n perpendicular l rightwards double arrow m parallel to n rightwards double arrow t h e space l i n e s space m space a n d space n space d o space n o t space i n t e r s e c t T h i s space i s space a space c o n t r a d i c t i o n space t o space t h e space f a c t o r space t h a t space t h e space l i n e s space m space a n d space n space p a s s space t h r o u g h space t h e space p o i n t space P H e n c e space o u r space a s s u m p t i o n space t h a t space t h r o u g h space a space g i v e n space p o i n t space t w o space p e r p e n d i c u l a r space l i n e s c a n space b e space d r a w n space t o space a space g i v e n space l i n e space i s space i n c o r r e c t. T h e r e f o r e comma space t h r o u g h space a space g i v e n space p o i n t comma space o n l y space o n e space p e r p e n d i c u l a r space c a n space b e space d r a w n space t o space a space g i v e n space l i n e.

Answered by Vimala Ramamurthy | 14th Sep, 2014, 11:02: AM