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# Reflection, Rotation, Translation

There are three basic transformations that can be done to a shape:

1. Reflection (flip)

2. Rotation (turn)

3. Translation (slide)

These transformations move the shape without making any changes to its shape or size.

Lets discuss them further:

1. Reflection – A reflection flips a shape over to create a mirror image.

In this example, the triangle on the right has been reflected (flipped) over the dotted line to create a mirror image. The vertices of the triangle A, B, and C has been reflected (flipped) over the dotted line to create the mirror image as another triangle having vertices A’, B’ and C’.

Notice that the second figure (which is called the image) is exactly opposite of the original figure, because it appears to be reflected, as in a mirror. When you look in a mirror, you look at your mirror image which is a reflection. It looks identical but is the opposite of the original image. For example, if you have something written on your shirt, it reads backward in the mirror.

The dotted line is called the line of reflection. It is also sometimes referred to as the axis of  reflection or the mirror line.

The original point A and the new point A’ are the exact same distance (3 units) from the line of reflection. The same is true for points B’ (1 unit away) and point C’ (3 units away). Whenever a shape is reflected, each set of the corresponding must be the same distance from the line of reflection.

We know about the reflection in a mirror but do you know that they also occur in water. However, a reflection in water is not the exact reflection. This is because the image in the water is normally somewhat distorted. Hence, it is not the exact same size and shape.

2. Rotation – A rotation turns a shape.

In this example, the triangle has been turned or rotated.

In some cases, the shapes are rotated just a few degrees, while in other cases, they may be rotated significantly. In this example, the triangle is rotated counter-clockwise.

Whenever a rotation occurs, the object must always stay the same size and the same   shape. There is always a point about which the shape is turned – like the center of a clock about which the minute and second hands move. In this example, that point is marked with the crosshairs.

If a figure is rotated all the way around, back to where it started, this is called a full rotation and is 360°. When a figure is rotated halfway around, it is 180°.

When a figure is rotated exactly 180°, it is said to have point symmetry because each point has a matching point which is the same distance but in the opposite direction

3.Translation – A translation moves or slides a shape.

In this example, the rectangle has been translated (moved or slid). The vertices of the rectangle A, B, C, and D has been translated (moved or slid) to the points A’, B’,C’ and D’, as shown in the above figure.

The new rectangle (called the image) has been moved up and to the right.

A translation always moves an object but it does not turn it, flip it, or change its size.

All points move the same distance and the same direction.

In the above figure, each point was moved 9 spaces to the left and 4 spaces up.

Let's take a look at some more examples:

Determine whether each picture represents a reflection, rotation, or translation.

1)

Answer) This is a translation because the figure has been moved or slid.

2)

Answer) This is a reflection because the triangle has been flipped over the line.

3)

Answer) This is a rotation because the figure has been turned.

Summary

These transformations move a shape without making any changes to its shape or size.

1) Reflection – A reflection flips a shape over to create a mirror image.

2) Rotation – A rotation turns a shape.

3) Translation – A translation moves or slides a shape.

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