Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0404
A transformation is a change made to a figure. The original figure is called the preimage, while the transformed figure is called the image. When we slide a figure without changing the size or shape of the figure, it is said to be a translation. By using matrix addition, we can translate the vertices of a figure.
| EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), translate the preimage 5 units right and 3 units down. Then, sketch the image. |
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A dilation is a transformation that changes the size of a figure.
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EXAMPLE: Given triangle ABC where A (–2,0), B (0, 4) and C (2, 1) Increase the size of the triangle by a factor of 1.5. Then, sketch the image. |
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A reflection, or flip, is a transformation that creates symmetry on the coordinate plane. You can use matrix multiplication to graph reflections in the coordinate plane.
| Matrices for Reflections in the Coordinate Plane | |||
| Reflection in the y-axis | Reflection in the x-axis | Reflection in the line y = x | Reflection in the line y = –x |
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EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2),. Reflect the triangle across the y-axis. Then, sketch the image. |
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A rotation is a transformation that turns a figure about a fixed point called a center of rotation. You can rotate a figure as much as 360 degrees. In this text, all rotations are counterclockwise about the origin.
| Matrices for Rotations in the Coordinate Plane | |||
| Rotation of 90° | Rotation of 180° | Rotation of 270° | Rotation of 360° |
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EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2),. Rotate the triangle 270°. Then, sketch the image. |
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