cordinate geometry

Question

calculate the distance between the parallel lines 3x + 6y + 5 = 0 and 2x + 4y - 7 = 0

Answer 1

3x + 6y + 5 = 0 (divide by 3)

2x + 4y - 7 = 0  (divide by 2)

 

x+2y+5/3=0

x+2y-7/2=0

 

These two lines are parallel. The distance between two parallel lines

ax+by+c₁ and ax+by+c₂=0 is calculated as

d=|c₂-c₁|/√(a²+b²)=

=|5/3+7/2|/√(1+4)=31/(6√5).