Transformation of Graphs Using Matrices - Reflection

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage.

A reflection maps every point of a figure to an image across a line of symmetry using a reflection matrix.

Use the following rule to find the reflected image across a line of symmetry using a reflection matrix.

Example:

Find the coordinates of the vertices of the image of pentagon ABCDE with A (2, 4), B (4, 3), C (4, 0), D (2, –1), and E (0, 2) after a reflection across the y -axis.

Write the ordered pairs as a vertex matrix.

To reflect the pentagon ABCDE across the y -axis, multiply the vertex matrix by the reflection matrix .

Therefore, the coordinates of the vertices of the image of pentagon ABCDE are A '(–2, 4), B '(–4, 3), C '(–4, 0), D '(–2, –1), and E '(0, 2).

Notice that, both figures have the same size and shape.