Questions on Geometry: Length, distance, coordinates, metric length answered by real tutors!

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Question 164587This question is from textbook Geometry Glencoe Mathematics
: Find the distance between each pair of parallel lines
1. y= -3 y= 1
2. x= 4 x= -2
3. y=2x + 2 y= 2x - 3This question is from textbook Geometry Glencoe Mathematics
: Find the distance between each pair of parallel lines
1. y= -3 y= 1
2. x= 4 x= -2
3. y=2x + 2 y= 2x - 3
Answer by Fombitz(1789) About Me  (Show Source):
You can put this solution on YOUR website!
1. Each block is 1 unit. Distance is 4 units.
drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line( -100,-3,100,-3)),<BR> green(line(-100,1,100,1)))
2.Distance is 6 units.
drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line( -2,-100,-2,100)),<BR> green(line(4,-100,4,100)))

3.This distance takes a little bit more work.
.
.
.
drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line( -5,-8,5,12)),<BR> green(line(-5,-13,5,7)))
A line perpendicular to the parallel lines will have a slope that satisfies this relationship,
m[1]m[2]=-1
2*m[2]=-1
m[2]=-1/2
The equation of the line that has that slope and goes through point (0,2) (that is, intersects y=2x+2 at (0,2))is
y-y[p]=m(x-x[p])
y-2=-(1/2)x
y=-(1/2)x+2
This new line intersects line y=2x-3 at the following x,
2x-3=-(1/2)x+2
2.5x=5
x=2
with corresponding y,
y=2x-3
y=4-3=1
Intersects at (2,1)
drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle(0,2,.2),circle(2,1,0.2),blue(line(2,1,0,2)),green(line( -5,-8,5,12)),<BR> green(line(-5,-13,5,7)))
The distance between the lines equals the distance between (0,2) and (2,1).
D^2=(x[1]-x[2])^2+(y[1]-y[2])^2
D^2=(0-2)^2+(2-1)^2
D^2=4+1
D=sqrt(5)