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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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!

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.

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.

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.

You measure the distance from each point to the mirror line and place a point directly opposite on the other side of the mirror line the same distance away from it. So, in our case, we can see that point B is 5 units away from the mirror line (see video). That means we have to measure 5 units from the mirror line to the opposite side of the page and place a point there. Point C is 6 units away from the mirror line. Again, we place a point opposite of this, on the other side of the mirror line, 6 units away from the mirror line. We do the same thing for point A. This point is 2 units away from the mirror line. What does that mean? That means we place a point 2 units away from the mirror line to the left of the mirror line.

Now, all we have to do is connect the dots to draw in our reflected triangle.

You see? Even though the shape seemed harder in the beginning, all you really have to do is simplify the shape to a bunch of points, then reflect them, then connect the dots, and you've got a reflected image of a simple shape!

Now, you're a pro at reflecting simple shapes using a mirror line! Remember, a **reflection** is the flipping of a figure or a point over a line of reflection. A reflection does not change size, and it faces the other way.

To reflect a dot or a simple shape, measure each point's distance away from the mirror line using a line drawn from the original point and to the mirror line in a perpendicular fashion. Take this distance, and measure out the same distance in a perpendicular fashion to the mirror line on the opposite side of the mirror line, and place the reflected point there.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Reflection, Rotation & Translation 4:23
- Reflecting Simple Shapes in a Mirror Line 3:37
- Graphing Translations & Finding a Set of Coordinates 3:45
- Rotating Shapes by Degrees, Center & Direction 4:19
- How to Graph Reflections Across Axes, the Origin, and Line y=x 6:07
- Go to 6th-8th Grade Geometry: Transformations

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