Distance between two parallel lines

Hey kiddo, let's talk about the distance between two parallel lines! Imagine you draw two lines on a piece of paper, and they never ever meet each other, they look like train tracks, right? Well, we call them parallel lines!

Now, let's say we have a point (a dot) anywhere on the paper. How can we tell which of the two lines is closest to our point? Here's how: we draw a line that starts from our point and goes straight up (or down) until it hits one of the parallel lines. We are only focusing on the line that goes straight up (or down).

When this line hits one of the parallel lines, it will create a little triangle. Remember triangles? Just like the ones we draw in our math class! Now, the distance between our point and the closest parallel line is the length of this little triangle we just made, from the point straight up (or down) to the parallel line.

To find this length, we can use a formula! It's called the distance formula:

distance = |Ax + By + C| / √(A² + B²)

Don't worry, we can break it down:

- A and B are the numbers that sit in front of x and y in the equation of the parallel lines (remember the equation y = mx + b from math class?).
- C is just a number on its own, it's like having a coffee cup without any coffee in it, it's just there!
- | | means absolute value, which is like taking the positive version of a number (so if we get a negative answer, we make it positive).
- √ is the square root button on the calculator!

So, all we need to do is put the A, B, and C values from the equations of the parallel lines into the formula, and voila! We get the distance between the point and the closest parallel line. Easy peasy, lemon squeezy!