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Definitions about transformations.

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Mathematics Vectors & transformations

The four transformations ,[object Object],[object Object],[object Object],[object Object],[object Object],The word TERRY: only to remember the 4 types. You must specify all the details for each type.

TRANSLATION ,[object Object],[object Object],[object Object],[object Object]

ENLARGEMENT ,[object Object],[object Object],[object Object],[object Object]

ROTATION ,[object Object],[object Object],[object Object]

REFLECTION ,[object Object],[object Object],[object Object]

Vectors A vector is an ordered pair of numbers that can be used to describe a translation. The notation is: Where a is the distance moved in the +X direction. And b is the distance moved in the +Y direction.

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The triangle DEF --> TRIANGLE HIG is a glide reflection. Reflection line: Each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. In other words, the line of reflection lies directly in the middle between the figure and its image -- it is the perpendicular bisector of the segment joining any point to its image. The reflection line = IG Translation rule: The translation rule is shift. Shifts A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged. A horizontal shift adds/subtracts a constant to/from every x-coordinate while leaving the y- coordinate unchanged. Vertical and horizontal shifts can be combined into one expression. Shifts are added/subtracted to the x or f(x) components. If the constant is grouped with the x, then it is a horizontal shift, otherwise it is a vertical shift. center and angle of rotation: Glide translation rule:and reflection line: When a translation (a slide or glide) and a reflection are performed one after the other, a transformation called a glide reflection is produced. In a glide reflection, the line of reflection is parallel to the direction of the translation. It does not matter whether you glide first and then reflect, or reflect first and then glide. This transformation is commutative. When two or more transformations are combined to form a new transformation, the result is called a composition of transformations. Since translations and reflections are both isometries, a glide reflection is also an isometry. Solution The triangle DEF --> TRIANGLE HIG is a glide reflection. Reflection line: Each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. In other words, the line of reflection lies directly in the middle between the figure and its image -- it is the perpendicular bisector of the segment joining any point to its image. The reflection line = IG Translation rule: The translation rule is shift. Shifts A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged. A horizontal shift adds/subtracts a constant to/from every x-coordinate while leaving the y- coordinate unchanged. Vertical and horizontal shifts can be combined into one expression. Shifts are added/subtracted to the x or f(x) components. If the constant is grouped with the x, then it is a horizontal shift, otherwise it is a vertical shift. center and angle of rotation: Glide translation rule:and reflection line: When a translation (a slide or glide) and a reflectio.

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Mathematics

1. Mathematics Vectors & transformations

2.

3.

4.

5.

6.

7. Vectors A vector is an ordered pair of numbers that can be used to describe a translation. The notation is: Where a is the distance moved in the +X direction. And b is the distance moved in the +Y direction.