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Published byChristal Phillips Modified over 6 years ago

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Properties of Reflections

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Warm up

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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

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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.

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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.

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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.

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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.

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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.

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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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