What is the distance between the parallel lines having equations 2x+2y=16 and x+y=0?

I'm getting 2 as my answer but the answer is supposed to be 4√2

find slope of perpendicular

original is slope = -1
so slope of perpendicular is
-1/-1 = 1

pick a point on line 2, like (0,0)
then equation of perpendicular through that point is
y = x (just to make it east)
where does y = x hit the first line?
2 x + 2 x = 16
x = 4
then y = 4
so
distance form(0,0) to (4,4)
sqrt (4^2 + 4^2 ) = sqrt (2*16)
= 4 sqrt 2

Hey, Damon, can you please look at my reply on my problem?

Beats me Ryan

thanks!

To find the distance between two parallel lines, you need to first determine a point on one of the lines and then find the perpendicular distance between that point and the other line.

Let's start with the first equation, 2x + 2y = 16. We can rearrange this equation to solve for y: y = (16 - 2x) / 2. Now, let's choose a value for x that makes calculation easier. Let's set x = 0, which gives us y = 8. So, we have a point (0, 8) on the first line.

Now, we need to find the perpendicular distance from this point to the second line, x + y = 0. We can find the equation of the perpendicular line that passes through the point (0, 8) by taking the negative reciprocal of the slope of the second line. The second line can be rewritten as y = -x. The slope of this line is -1. Therefore, the slope of the perpendicular line is 1.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through (0, 8) as y - 8 = 1(x - 0), which simplifies to y - 8 = x. Rearranging this equation, we get x - y + 8 = 0.

To find the intersection point between the two lines, we can solve the system of equations: 2x + 2y = 16 and x - y + 8 = 0. Solving these equations simultaneously, we get x = 2 and y = -2.

Now that we have the coordinates of the intersection point, we can find the distance between this point and the line x + y = 0. Using the formula for the distance between a point (x1, y1) and a line Ax + By + C = 0, the distance (d) is given by the formula:

d = |Ax1 + By1 + C| / √(A^2 + B^2)

For the line x + y = 0, A = 1, B = 1, and C = 0. Plugging in the values, we get:

d = |1(2) + 1(-2) + 0| / √(1^2 + 1^2)
d = 4 / √2

Therefore, the distance between the parallel lines 2x + 2y = 16 and x + y = 0 is 4√2.