Which rigid motion does not preserve orientation?

Okay, so you’re diving into the world of geometry, right? Think about rigid motions – these are moves that keep shapes exactly the same size and shape. We’re talking translations (slides), rotations (turns), reflections (flips), and those slightly weird glide reflections. But here’s the kicker: not all of these play nice with a shape’s “orientation.”

What’s “orientation,” you ask? Good question! Imagine you’ve drawn a triangle, labeling the points A, B, and C in that order going clockwise. Orientation is just the order of those points. Some motions keep that order the same. Others? Not so much.

Translations and rotations? They’re the good guys. Slide your triangle across the page, or spin it around a point, and A is still followed by B, which is followed by C. Clockwise remains clockwise. Easy peasy.

Now, let’s talk about reflections. This is where things get interesting. Picture holding that triangle up to a mirror. Suddenly, the order of the points is reversed! What was clockwise is now stubbornly counter-clockwise. A reflection flips the orientation, plain and simple. Glide reflections? They’re just reflections with an extra slide thrown in, so they also flip that orientation.

I remember back in high school, I was totally tripped up by this. It seemed so obvious once I understood it, but visualizing it really helped. Grab a piece of paper, draw a shape, label the points, and then actually do the transformations. You’ll see it for yourself.

Bottom line? Translations and rotations keep your shape’s “clockwise-ness” or “counter-clockwise-ness” intact. Reflections and glide reflections? They’re the rebels, flipping the order and giving you a mirror image with a reversed orientation. It’s a small detail, but it makes a big difference in how we understand geometric transformations.