SOLUTION: Find the distance between the pair of parallel lines. y= 4x + 4 y= 4x - 4 Answer options: a)2.01 b)2.2 c)1.94 d)2.37 This was from a recent math test I took and I can't fig

Algebra ->  Length-and-distance -> SOLUTION: Find the distance between the pair of parallel lines. y= 4x + 4 y= 4x - 4 Answer options: a)2.01 b)2.2 c)1.94 d)2.37 This was from a recent math test I took and I can't fig      Log On


   

Question 995643: Find the distance between the pair of parallel lines.
y= 4x + 4
y= 4x - 4
Answer options: a)2.01 b)2.2 c)1.94 d)2.37
This was from a recent math test I took and I can't figure out how to solve. I have a chapter test coming up and want to prepare.
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Try to think of a strategy.

First equation has y-intercept at 4, and second equation has y-intercept at -4.

A line perpendicular to both lines will have a segment which is the distance between the two lines.

Line perpendicular to y=4x%2B4 passing through (0,4) will be y=-%281%2F4%29%2Bb and you can find this b;

y%2B%281%2F4%29x=b
b=y%2B%281%2F4%29x
b=4%2B%281%2F4%29%2A0
b=4 which you might have figured without calculation.
This perpendicular line's equation is y=-%281%2F4%29x%2B4

Find the point of intersection of y=-%281%2F4%29x%2B4 and y=4x-4.

--more later, maybe---

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=+4x+%2B+4
y=+4x+-+4
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x+%2B+4%2C+4x+-+4%29+
to find the distance between the pair of parallel lines first find perpendicular line and its intersection points with given parallel lines
given parallel lines have same slope and it is m=4
y-intercept of first line is at (0,4) and
y-intercept of second line is at (0,-4)
so, the perpendicular line will have a slope negative reciprocal to m=4 and it is m%5Bp%5D=-1%2F4
use the slope and y-intercept of first line is at (0,4) to find the equation of the line perpendicular to the line y=+4x+%2B+4
The equation of the line that has that m%5Bp%5D=-1%2F4 and goes through point (0,4) is:
y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-4=-%281%2F4%29x
y=-%281%2F4%29x%2B4

so, the lines y=+4x+%2B+4 and y=-%281%2F4%29x%2B4 are perpendicular to each other and intersect at (0,4)
now we need to find intersection point of the lines y=+4x-4 and y=-%281%2F4%29x%2B4
equal right sides and solve for x
+4x-4=-%281%2F4%29x%2B4
+4x%2B%281%2F4%29x=4%2B4
+4x%2Bx%2F4=8
+4%2A4x%2B4x%2F4=8%2A4
+16x%2Bx=32
+17x=32
+x=32%2F17
+x=1.882352941176471
+x=1.9
with corresponding y,
y=4x-4
y=4%2A1.9-4=3.6

so, the lines y=+4x-4 and y=-%281%2F4%29x%2B4 intersect at (1.9,3.6)



now, find the distance between points (0,4) and (1.9,3.6); that will be the distance between given parallel lines

d%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
d%5E2=%280-1.9%29%5E2%2B%284-3.6%29%5E2
d%5E2=%28-1.9%29%5E2%2B%280.4%29%5E2
d%5E2=3.61%2B0.16
d%5E2=3.77
d=1.94164878389476
d=1.94

so, your answer is c)1.94

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Find the distance between the pair of parallel lines.
y= 4x + 4
y= 4x - 4
Answer options: a)2.01 b)2.2 c)1.94 d)2.37
This was from a recent math test I took and I can't figure out how to solve. I have a chapter test coming up and want to prepare.
The distance between these 2 lines is the perpendicular line drawn to both lines

Slope of perpendicular line to y = 4x + 4 or y = 4x - 4: -+1%2F4

1) Using this slope and point (0, 4), determine the equation of the line that's equidistant from these 2 lines

2) Determine the point at which the perpendicular line intersects the line: y = 4x - 4

3) With the two coordinate points where the perpendicular line intersects both lines, use the distance formula to find the distance between the 2 lines

4) You should get distance as: 1.938501 ≈ highlight_green%281.94%29 (CHOICE c)