SOLUTION: Two parallel lines y=-2x+2 and y=-2x-3 are intersected by a transversal with slope 1/2 which crosses the y axis at 2. What is the distance between the two points where the transver

Algebra ->  Algebra  -> Angles -> SOLUTION: Two parallel lines y=-2x+2 and y=-2x-3 are intersected by a transversal with slope 1/2 which crosses the y axis at 2. What is the distance between the two points where the transver      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 179846: Two parallel lines y=-2x+2 and y=-2x-3 are intersected by a transversal with slope 1/2 which crosses the y axis at 2. What is the distance between the two points where the transversal intersects the parallel lines?
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
The transversal has slope 1/2 and passes through (0,2)[y-intercept].So,
y-2=x/2
2y-4=x
x=2y-4
Subtituting this to y=-2x+2,
y=-2(2y-4)+2
y=(-4y+8)+2
y=-4y+10
5y=10
y=2
x=2y-4=2(2)-4=4-4=0 The point of intersection is (0,2)
Substituting x=2y-4 to y=-2x-3,
y=-2(2y-4)-3
y=(-4y+8)-3
y=-4y+5
5y=5
y=1
x=2y-4=2(1)-4=2-4=-2 The point of intersection is (-2,1)
The distance between (0,2) and (-2,1)
d=sqrt%28%280%2B2%29%5E2%2B%282-1%29%5E2%29=sqrt%282%5E2%2B1%5E2%29=sqrt%284%2B1%29=sqrt%285%29

Power up,
HyperBrain!
Stop this mess! Click here