Question

Find the equation of the line perpendicular to the line 2x + y - 1 is equal to zero and passing through the point of the intersection of the line x + 2 y - 1 is equal to zero and y is equal to x

Answer 1

Heya©®©®©©®©®©®©©

______________________________

EQUATION OF A LINE PASSING THROUGH THE INTERSECTION OF TWO LUNES IS GIVEN BY

A1 + K A2 = 0

WHERE A1 = x + 2y -1 = 0

AND

A² = y - x = 0

___________________________________

x ( 1 - k ) + y ( 2 + k ) - 1 = 0

NOW IT IS GIVEN THAT THIS LINE IS PERPENDICULAR TO 2x + y - 1 = 0

=>

( k - 1 ) / ( 2 + k ) = -2

=>

k - 1 = -4 - 2k

=>

3k = -3

=>

k = -1

=>

x ( 1 + 1 ) + y ( 2 -1 ) -1 = 0

=>

2x + y -1 = 0

SO, EQUATION OF A LINE PASSING THROUGH THE INTERSECTION OF TWO GIVEN LINES AND PERPENDICULAR TO THE GIVEN LINE IS

2x + y -1 = 0