SOLUTION: 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

Algebra ->  Length-and-distance -> SOLUTION: 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      Log On


   

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 - 3 This question is from textbook Geometry Glencoe Mathematics

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. Each block is 1 unit. Distance is 4 units.

2.Distance is 6 units.


3.This distance takes a little bit more work.
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.
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A line perpendicular to the parallel lines will have a slope that satisfies this relationship,
m%5B1%5Dm%5B2%5D=-1
2%2Am%5B2%5D=-1
m%5B2%5D=-1%2F2
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%5Bp%5D=m%28x-x%5Bp%5D%29
y-2=-%281%2F2%29x
y=-%281%2F2%29x%2B2
This new line intersects line y=2x-3 at the following x,
2x-3=-%281%2F2%29x%2B2
2.5x=5
x=2
with corresponding y,
y=2x-3
y=4-3=1
Intersects at (2,1)

The distance between the lines equals the distance between (0,2) and (2,1).
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
D%5E2=%280-2%29%5E2%2B%282-1%29%5E2
D%5E2=4%2B1
D=sqrt%285%29