Determine the diameter of the largest circle that can be drawn between the parallel lines y=2x and y=2x-5.

Answer 1

What is the distance between them?

find the perpendicular line

y=-1/2 x + b
pick a point on the first line: say, 1,2
2= -1/2 *1+b
b=2.5
y= -.5x+2.5 is the perpendicular line.
now, what point does this line intersect the second parallel line?
y=-.5x+2.5
y=2x-5
or 2x-5=-.5x+2.5
2.5x=7.5
x=3
y=2x-5=1
distance between points 1,2 and 3,1
d= sqrt (2^2 + 1^2)=sqrt5
check all that math, I did it in my head.