Properties of Reflections

Warm up

Triangle ABC has vertices A(1, 1), B(3, 1), and C(2, 4). Describe how

each reflection changes the coordinates of the vertices of the

preimage to create the coordinates of the vertices of the image:

(1) across the x-axis(2) across the y-axis

How do you describe the properties of reflection and their effect on the

congruence and orientation of figures?

Reflections preserve size and shape, but not orientation.

Translations and reflections are both types of transformations.

While a translation does not change the orientation of a figure,

a reflection does. A line of reflection is often one of the axes,

but it can be any line, including lines that are not horizontal or

vertical.

What characteristics do you look for in an image to know that it has been reflected

from a preimage?

The corresponding sides have the same lengths, and the corresponding angles

have the same measures. The shape and size of the image is the same as that of

the preimage. The only difference is the image is a mirror image of the preimage.

To avoid plotting the vertices of the image correctly but labeling them

incorrectly, label each vertex of the image as you plot the point and confirm that each letter matches the letter of the corresponding

vertex in the preimage.

How do the coordinates of the image differ from the coordinates of the preimage when a figure is

reflected across the y-axis?

The x-values are the opposite of the preimage’s x-values, but the y-

values remain the same.

How do you know when a transformation is a reflection?

The image will have the same size and shape as the preimage, but the orientation will not be the same. There will be a line of reflection

such that each image point will be the same distance from that line as its corresponding preimage point.

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