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Unit 5

Unit 5. Transformations in the Coordinate Plane. There are 3 main types of transformations we will look at in this chapter

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Unit 5

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  1. Unit 5 Transformations in the Coordinate Plane

  2. There are 3 main types of transformations we will look at in this chapter • Translation: Any figure which is moved from one location to another location on the coordinate plane without changing its shape, size, or orientation is called translation. • Example: http://www.hstutorials.net/math/geometry/definitions/translation.htm Practice: Translate each figure as instructed below. Describe using words (up, down, left, right) how the figures were translated. 1. 2.

  3. Warm-up • 1. 2.

  4. The next type of transformation we will look at is called a reflection. A reflection flips an object or shape across a specific line. • Example: http://www.youtube.com/watch?v=j1X_UIOvEwA • Practice: Reflect the image below as instructed. 1. Reflect over the x-axis 2. Reflect over the y-axis

  5. While reflecting over the x or y axis is a very common way to reflect objects. We can also reflect shapes over any line (not just an axis). Examples: of reflecting over a horizontal or vertical line 1. Reflect over 2. Example of reflecting over a non-horizontal or non-vertical line. 3. Reflect over Notice that the coordinates (x,y) from the first shape end up being flipped (y,x) in the second shape. When reflecting over the line you flip the x and y and change the sign.

  6. practice1. reflect over 2. reflect over 3. Reflect over 4. reflect over

  7. The last type of transformation we will look at is called a rotation. A Rotation is a transformation that turns a figure about a fixed point. • There are 3 important things we need to know before rotating an object • Point of rotation • Angle of rotation • Direction of rotation Example: http://www.youtube.com/watch?v=YkQQBH21GiQ The point of rotation is usually the origin, but sometimes might be a point on the shape. The angle of rotation will be in increments of 90˚ (90˚, 180˚, 270˚) The direction will either be clockwise (the way a clock turns) or counter clockwise (the opposite way a clock turns).

  8. 90̊ = 1 turn 180̊ = 2 turns 270˚ = 3 turns clockwise = right counter-clockwise = left • Tip: When rotating you can turn the paper sideways depending on which direction and how many degrees the rotation is. Then copy down the coordinates looking at the graph the way it is, and turn it back to its original position and graph the new coordinates. • Example: Rotate 90˚ clockwise about the origin. 90˚ turn clockwise 180˚ turn clockwise 270˚ turn clockwise

  9. Practice • rotate 90̊clockwise about the origin 2. rotate 90˚ counter-clockwise about the origin 3. rotate 180˚ about the origin 4. rotate 270˚ clockwise about the origin

  10. An isometry a transformation to an object or shape that preserves distances between the points of the shape. A rotation, reflection or translation are all examples of an isometry, since the distances between two points on the plane remain the same afterwards. • A dilation increases or decreases the size of a shape or object. A dilation is NOT an isometry because distance between points is not preserved. • Example of a dilation Because of the dilation to the y values (2y) you can see the distances between the points does not stay the same. Therefore this is not an isometry.

  11. How to rotate around a point that is NOT the origin Example: Rotate 90˚ counter clockwise around the point 1st: Graph the point that we want to rotate around. 2nd: Going through the point draw a horizontal line, and a vertical line. 3rd: Now rotate the paper and use the new lines as the x and y axis to reference where our new shape goes. 4th: Graph the new shape

  12. Practice 1) 180˚ around the point 2) 90˚ CCW around the point 3) 270˚ CW around the point 4) 90˚ CW around the point

  13. Warm-up: Perform all the transformations in order. Each time using the new shape as the object you are transforming. reflect over the line then Rotate around the origin 90˚ cw

  14. Mapping is the description of the transformation that puts one given shape exactly on top of another given shape. Example: What transformation maps the shaded figure onto the non-shaded figure. Tips: Remember A translation will not change the orientation of the shape. It will simply move the shape up, down, left and right. A reflection flips a shape across a line changing its orientation from being flat to tall or from facing one direction to facing the opposite. A rotation or 90˚ or 270˚ will cause the shape to turn onto its side. A rotation of 180˚ will flip a shape upside down (however, with squares and rectangles you cant tell). Answer: This is clearly a translation: (x,y) to (x+4, y+4)

  15. Practice: Describe the transformations that maps the shaded figure onto the non shaded figure. 1. 2. 3.

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