What is the perpendicular of 2?

The Perpendicularity Puzzle: What’s the Deal with 2?

Okay, so you’ve heard of “perpendicular,” right? It’s all about lines meeting at perfect right angles. But then someone throws you a curveball: “What’s the perpendicular of… 2?” Sounds kinda weird, doesn’t it? Well, it’s actually a pretty cool question that gets to the heart of how numbers, lines, and slopes are all connected.

First, a super-quick refresher. Think of a line on a graph. Its slope is just how steep it is – basically, how much it goes up (or down) for every step you take to the side. We usually say “rise over run.” Now, a horizontal line? Totally flat, right? That means its slope is zero. And a vertical line? Good luck trying to run across that – its slope is undefined because you’d be dividing by zero, which is a big no-no in math.

Now, here’s where it gets interesting. Perpendicular lines are lines that meet at a perfect 90-degree angle. The secret? Their slopes are negative reciprocals of each other. Sounds like a mouthful, I know! But it just means you flip one slope upside down (that’s the reciprocal part) and then change its sign (that’s the negative part). So, if you’ve got a line with a slope of, say, m, then any line perpendicular to it will have a slope of -1/m. Trust me, it works! The product of their slopes will always be -1.

So, back to our friend, the number 2. How do we even begin to think about the perpendicular of a single number? Well, let’s imagine that 2 is a slope. Think of it as a line that goes up two steps for every one step forward. To find the slope of a line that’s perpendicular to that line, we gotta do the negative reciprocal thing.

First, flip it! 2 (or 2/1) becomes 1/2. That’s the reciprocal. Piece of cake!

Next, make it negative. So, 1/2 becomes -1/2.

Boom! The “perpendicular of 2” is -1/2. Seriously, that’s it. Any line with a slope of -1/2 will be at a perfect right angle to a line with a slope of 2.

Of course, there are a couple of weird exceptions. A line that’s perfectly flat (horizontal, slope of 0) is perpendicular to a line that’s perfectly upright (vertical, undefined slope). And vice versa. Think of it like the horizon meeting a skyscraper – a classic perpendicular combo.

So, to wrap it all up: When someone asks you for the “perpendicular of 2,” they’re really asking for the negative reciprocal, which is -1/2. It’s all about how lines and slopes play together, and it’s a neat little trick to have up your sleeve. You can even impress your friends at parties with this one! Okay, maybe not parties, but definitely at your next math study group.