What are two lines that are perpendicular?

Perpendicular Lines: Straight Talk About Right Angles

Ever wondered what makes two lines “perpendicular”? It’s simpler than you might think! In the world of geometry, it basically means they meet at a perfect right angle – that crisp 90-degree corner you see all the time. The word itself comes from Latin, “perpendicularis,” which referred to a plumb line. Think of it as perfectly upright.

So, what exactly does it mean for lines to be perpendicular? Well, they have to intersect, and when they do, that intersection has to form a 90-degree angle. You know, like the corner of a square. That little square symbol you sometimes see at the intersection? That’s the universal sign for a right angle, and it tells you the lines are perpendicular. The cool thing is, it works both ways: if line A is perpendicular to line B, then line B is definitely perpendicular to line A. They’re a team! You’ll often see this written as AB ⊥ CD, which just means line AB is perpendicular to line CD.

How can you spot these perpendicular lines in the wild? Easy! Just look for that tell-tale right angle. But what if you’re dealing with lines on a graph? Then you can use their slopes. This is where it gets a little math-y, but stick with me.

Slopes: The Secret Code

Perpendicular lines have a special relationship when it comes to their slopes. They’re negative reciprocals of each other. Sounds complicated, right? It just means that if one line has a slope of, say, 2, the line perpendicular to it will have a slope of -1/2. Flip it and switch the sign! Another way to think about it: if you multiply the slopes of two perpendicular lines, you’ll always get -1. It’s like a secret handshake!

A Couple of Quirks

Now, here are a couple of special cases to keep in mind. A vertical line and a horizontal line? Always perpendicular. No question. Vertical lines, bless their hearts, have an undefined slope. And horizontal lines? Their slope is always zero.

Finding the Equation: A Practical Example

Okay, let’s say you want to find the equation of a line that’s perpendicular to another line and passes through a specific point. How do you do it? Let’s say we want to find a line perpendicular to y = −4x + 10 that passes through the point (7,2). First, spot the slope of the original line. In this case, it’s -4. Then, calculate the negative reciprocal. That’s 1/4. Finally, use the point-slope form (y – y1 = m(x – x1)) to build the equation of your new line. Plug in the point (7,2) and the slope 1/4, and you get y – 2 = (1/4)(x – 7). Simplify that, and you’re left with y = x/4 + 1/4. Boom! You’ve got your perpendicular line.

Perpendicular Lines in Real Life

Honestly, perpendicular lines are everywhere. Think about the corners of a picture frame, the walls in your house, even the way streets intersect in a city grid. The letter “L” is a classic example! Once you start looking, you’ll see them all over the place.

Beyond Basic Lines

And it doesn’t stop with just lines! You can also have a line perpendicular to a plane. Imagine a flagpole standing straight up on the ground. That flagpole is perpendicular to the plane of the ground. Or, you can even have two planes that are perpendicular to each other, like two walls meeting in a room. It’s right angles all the way down!