Question

find the distance between the lines 3x+4y+6=0 and 6x+8y-11=0​

Answer 1

Answer:

First of all we find the slopes of the two lines. We convert

the equations into slope intercept form

3x+4y=9⟹4y=−3x+9⟹y=−34x+94

6x+8y=15⟹8y=−6x+15⟹y=−68x+158

⟹y=−34x+158

slope m of the lines=−34

Hence both lines are parallel

Y intercept of the first line =94

Y intercept of the second line =158

Difference between the y- intercepts=∣∣∣94−158∣∣∣

=∣∣∣188−158∣∣∣

=38

1+m2−−−−−−√=1+916−−−−−−√=2516−−−√=54

Distance between the lines =38÷54=38×45=310