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Reflections are everywhere ... in mirrors, glass, and here in a lake.
... what do you notice ?

Every point is the same distance from the central line !
... and ...
The reflection has the same size as the original image.

The central line is called the Mirror Line:

Can A Mirror Line Be Vertical?

Yes. Here my dog "Flame" shows a Vertical Mirror Line (with a bit of photo editing).

You can try reflecting some shapes about different mirror lines here:

How Do I Do It Myself?

Just approach it step-by-step. For each corner of the shape:

1. Measure from the point to the mirror line (must hit the mirror line at a right angle)

2. Measure the same distance again on the other side and place a dot.

3. Then connect the new dots up!

Labels

It is common to label each corner with letters, and to use a little dash (called a Prime) to mark each corner of the reflected image.

Here the original is ABC and the reflected image is A'B'C'

Some Tricks

X-Axis

When the mirror line is the x-axis
we change each (x,y) into(x,−y)

Y-Axis

When the mirror line is the y-axis
we change each (x,y) into(−x,y)

Fold the Paper

And when all else fails, just fold the sheet of paper along the mirror line and then hold it up to the light !

6716, 6717, 3346, 3344, 3345, 3347, 5152, 5153, 841, 842

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Learn about reflection in mathematics: every point is the same distance from a central line.

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Note: here we call it resizing, but other people call it dilation, contraction, compression, enlargement or even expansion! Same idea, just different names.

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"Rotation" means turning around a center:

The distance from the center to any point on the shape stays the same.

Every point makes a circle around the center:

Here a triangle is rotated around
the point marked with a "+"

Try It Yourself

Here you can drag the pin and try different shapes:

And here you can choose an angle and see how to rotate different shapes point-by-point. Try and follow what happens each time:

6712, 6713, 6714, 6715, 839, 840, 2133, 2134, 3340, 3341

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The distance from the center to any point on the shape stays the same. Every point makes a circle around the center: Here a triangle is rotated around the point marked with a "+" Here you can drag the pin and try different shapes: And here you can choose an angle and see how to rotate different shapes point-by-point.

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In Geometry, "Translation" simply means Moving ...

... without rotating, resizing or anything else, just moving.

To Translate a shape:

Every point of the shape must move:

the same distance

in the same direction.

To see how this works, try translating different shapes here:

Note: You can translate either by angle-and-distance, or by x-and-y.

Try both to see what happens.

Writing it Down

Sometimes we just want to write down the translation, without showing it on a graph.

Example: to say the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write:

(x,y) → (x+30,y+40)

Which says "all the x and y coordinates become x+30 and y+40"

6720, 6721, 6722, 6726, 3348, 3349, 3350, 843, 2135, 2136

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In Geometry, "Translation" simply means Moving ... ... without rotating, resizing or anything else, just moving. To Translate a shape: Every point of the shape must move: the same distance in the same direction. To see how this works, try translating different shapes here: Note: You can translate either by angle-and-distance, or by x-and-y.

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Reflection practice problems

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Dilation practice problems

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Rotation practice problems

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Translation practice problems

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video tutorial on Reflections

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video tutorial on Dilations

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Dilation Of Objects On The Coordinate Plane

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video tutorial on Rotations

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video tutorial on Translations

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Transformations - Translating A Triangle On The Coordinate Plane