find the distance between the parallel lines x - 2y + 8 = 0 and 2x - 4y -2 = 0?

Answer 1

ewan

Answer 2

Line 1: x - 2y = -8 Line 2: x - 2y = 1 choose a point on Line 1: A(-8, 0) find the slope of these lines: m = 1/2 the slope of the line 3 that is perpendicular to these 2 lines: m' = -2 find the equation of line 3 passing through A(-8, 0): y = -2(x + 8), or 2x + y = -16 find the point of intersection B between Line 2 and 3: ie. solve x - 2y = 1 2x + y = -16 B(-31/5, -18/5) get the distance between A(-8, 0) and B(-31/5, -18/5) = sqrt((31/5 - 8)^2 + (1 8/5)^2) = sqrt((9/5)^2 + (18/5)^2) = 9/sqrt(5)

Answer 3

Line 1: x - 2y = -8
Line 2: x - 2y = 1
choose a point on Line 1: A(-8, 0)
find the slope of these lines: m = 1/2
the slope of the line 3 that is perpendicular to these 2 lines: m' = -2
find the equation of line 3 passing through A(-8, 0): y = -2(x + 8), or 2x + y = -16
find the point of intersection B between Line 2 and 3: ie. solve
x - 2y = 1
2x + y = -16
B(-31/5, -18/5)
get the distance between A(-8, 0) and B(-31/5, -18/5) = sqrt((31/5 - 8)^2 + (1 8/5)^2) = sqrt((9/5)^2 + (18/5)^2) = 9/sqrt(5)

Answer 4

Greetings,

Use the formula for distance between a point (xo,yo) and the
line ax + by + c = 0

This is the perpendicular distance and because the lines are parallel, slope -a/b = 1/2, this distance is also the distance between the lines.

d = |axo + byo +c | / sqrt(a^2 + b^2)

In this question choose a convenient point on the second line (1,0) and substitute into the formula of the first line

giving d = |1(1) -2(0) +8| /sqrt(1 + 4) = 9/sqrt(5) = 9 sqrt(5)/5

Regards

Answer 5

The two lines have slope of 1/2. Pick any line perpendicular to these two lines (its slope must be ?) and find where it intersects the two given lines. The distance between the points of intersection is the distance between the lines.

You should get (9√5)/5