Okay, this is a problem that I've tried over ten times before getting a fresh problem and trying that one too. I've never gotten a correct answer and I can't figure out why it's not right.
Here's the problem,
"Find the distance between each pair of parallel lines."
21.
y=2x+2
y=2x-3"
Could anyone explain to me how to do this problem? I've gotten through it completly, but I think I'm doing /something/ wrong.
Please help. =(
There are a couple ways to solve this problem.
The common method is to find a point on one line, then find it's distance to the other line. Let's find a point on y=2x+2. The point (x1,y1)=(0,2) is the most obvious one to use.
Now write the second equation as
ax+by+c=0 or
-2x+y+3=0
Then use the formula
distance = |a*x1 + b*y1 +c|/sqrt(a^2 + b^2)
where (x1,y1)=(0,2) a=-2, b=1 and c=3
We have distance=|-2*0 + 1*2 + 3|/sqrt(2^2 + 1^2) = 5/sqrt(5) = sqrt(5)
(That's the absolute value of the numerator.)
To find the distance between two parallel lines, the common approach is to find a point on one line and then calculate its distance to the other line.
In this problem, you are given two parallel lines:
1. y = 2x + 2
2. y = 2x - 3
To begin, let's find a point on the first line, y = 2x + 2. A point that lies on this line is (x1, y1) = (0, 2).
Next, rewrite the equation of the second line in the form ax + by + c = 0. The equation y = 2x - 3 can be rewritten as -2x + y + 3 = 0.
Now, we can use the formula for calculating the distance between a point (x1, y1) and a line in the general form. The formula is:
distance = |a*x1 + b*y1 + c| / sqrt(a^2 + b^2)
In this formula, we have a = -2, b = 1, c = 3, and (x1, y1) = (0, 2). Plugging these values in, we get:
distance = |-2*0 + 1*2 + 3| / sqrt((-2)^2 + 1^2)
= |0 + 2 + 3| / sqrt(4 + 1)
= |5| / sqrt(5)
= 5 / sqrt(5)
= sqrt(5)
So, the distance between the two parallel lines y = 2x + 2 and y = 2x - 3 is equal to sqrt(5).