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Transformations with Matrices
Chapter 4, Section 4
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Writing ordered pairs as matrices:
To write ordered pairs as a matrix, put the x values in row 1 and the y-values in row 2 (2,3) (4,5) (-1,8) (5,10) (-1,2) (3,4) (8,0) **original points are called the preimage, new points are called the image
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Types of Transformations
Translations – figure is moved up, down, left, or right Size, shape, and orientation do NOT change Dilations – figure changes size Shape and position do NOT change
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Types of Transformations
Reflections – figure is flipped over a line of symmetry Size and shape do NOT change Lines of reflections: y-axis, x-axis, line y=x Rotations – figure is moved around a center point Degrees of rotations: 90, 180, 270
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Some vocabulary: Vertex matrix – a matrix that consists of the original ordered pairs. Translation matrix – a matrix that shows how the figure is translated. *Will be the same size as vertex matrix*
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Translations Step 1: Vertex Matrix Step 2: Translation Matrix
Step 3: add the vertex matrix and the translation matrix together to get the new matrix Step 4: write the new ordered pairs from the new matrix – this is the answer 6
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Translation Example Translate triangle ABC 3 units left and 4 units up with vertices A(2, 3), B(-1, 4), C(0, 5) 7
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Dilations Step 1: Vertex Matrix Step 2: determine the scale factor
Step 3: multiply the scale factor by the vertex matrix to get the new matrix Step 4: write the new ordered pairs from the new matrix – this is the answer
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Dilation Example Find the coordinates of triangle ABC if the perimeter of triangle ABC is reduced by ½ with vertices A(2, 3), B(-1, 4), C(0, 5) 9
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Reflections Step 1: determine what line the figure is reflected over
Step 2: change the coordinates based on the line of reflection Step 3: write the new ordered pairs 10
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Demonstrating a Reflection
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Demonstrating a Reflection - Conclusions
When reflected over the x-axis: change the sign of the y values When reflected over the y-axis: change the sign of the x values When reflected over the line y=x: switch the x and y values
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Rotations Step 1: determine the degree to rotate the figure
Step 2: change the coordinates based on the degree of rotation Step 3: write the new ordered pairs **all rotations will be performed counter-clockwise 13
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Demonstrating a Rotation
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Demonstrating a Rotation- Conclusions
When rotated 90 degrees: switch the x and y values and change the sign of the new x values When rotated 180 degrees: change the sign of the x and y values When rotated 270 degrees: switch the x and y values and change the sign of the new y values
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Your turn: Classwork: Homework:
4-4 in practice workbooks. Homework: Transformations handout Exit Slip:Describe each of the transformations using only 1 word for each one.
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