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Geometric Transformations with Matrices

Geometric Transformations with Matrices. Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices. A transformation is a change made to a figure.

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Geometric Transformations with Matrices

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  1. Geometric Transformations with Matrices Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

  2. A transformation is a change made to a figure. • The original figure is called the preimage (A), while the transformed figure is called the image (A’). • 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. Translations

  3. 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.

  4. Quadrilateral ABCD has vertices A(0,0), B(-2,5), C(2,3) and D(4.1). Use a matrix to find the coordinates of the vertices of the image translated 5 units left and 2 units up. Then graph ABCD and A’B’C’D’.

  5. A dilationis a transformation that changes the size of a figure. EXAMPLE:  Given triangle ABC where A(–5,0), B(8,-1) and C(4,5)Find the coordinates of each image under the following dilations. Then graph the images.: a.) 4 b.) 1/5 c.) -1.5 Dilation

  6. A reflection, or flip, is a transformation that createssymmetry on the coordinate plane.  • You can use matrix multiplication to graph reflections in the coordinate plane. • 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. Reflections and Rotations with Matrices

  7. Rotations

  8. EXAMPLE: Given triangle ABC where A(-3,0), B (– 4,4) and C(1,1). Reflect the triangle across the y-axis, x-axis, y=x and y = -x. Then, sketch the image.

  9. EXAMPLE: Given quadrilateral ABCD where A(1, 1), B(3,1), C (6,4),and D(1,3). Rotate the quadrilateral: a.) 90 ° b.) 180° c.) 270° d.) 360° Then, sketch the image. For example…

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