Parallels and Distance

Question

Given the parallel lines   and  with equations      and     , respectively. 

Use the following questions to find the distance between the two lines. 

Find the line perpendicular to the two initial lines that passes through the point 

     

. Then enter the 

 

 and 

 

Find the point of intersection between line from Question 1 and line .

 

     ,     .

Answer 1

The slope of the perpendicular line is -1.

The line through (0,-1) is -1 = (y+1)/x

The intersection of this line with y=x+3 is (-2,1) (y=-x-1=x+3)

Now use the distance formula to get the distance d = sqrt[(x₁-x₂)²+(y₁-y₂)²]