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Reflecting Simple Shapes in a Mirror Line

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  • 0:01 Reflection
  • 0:41 Reflecting a Point
  • 1:26 Reflecting a Shape
  • 3:01 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
What is reflection? How can we reflect a shape over a line? You will learn about this as well as about the important properties of reflection as it relates to math!

Reflection

What do you see when standing in front of a mirror? Your reflection, of course! I think you'll agree that when you look at your reflection in a normal mirror, you don't change size. You're not any smaller or any bigger. You'll also notice that your reflection faces you. That means it faces the other way in relation to where you are faced.

In math, reflection is the flipping of a figure or a point over a line of reflection called the mirror line. When we reflect something over a mirror line it does not change size, and it faces the other way. It's as simple as that.

Let's go through two simple examples to demonstrate reflection.

Reflecting a Point

Let's start with something super easy. Take out a piece of graph paper and draw a line from the very top to the very bottom right at the center of the paper (see video). This will be our mirror line. To the right of the mirror line, draw a dot and call it A. From this dot, draw a line perpendicular to the mirror line. Measure the distance from the dot to the mirror line using this perpendicular line you just drew. In our case, it comes out to be two boxes or two units long.

That's all you need to know. Every point on one side of the mirror line will have the same distance from the mirror line on the other side. This means we need to measure two box lengths away from the mirror line on the opposite side and draw a dot there to complete our reflection of the point.

Reflecting a Shape

Okay, let's build on that then to something a little bit more challenging. Using this same paper, let's draw a triangle. A triangle is really just three points connected together with three different lines. How are we going to reflect triangle ABC?

Well, all we have to really do is simplify this shape to the three points. Just erase the lines in your head and you're left with point A, point B, and point C. You already know how to reflect one point, so now just do the same thing we did in the last section, but point by point.

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