UNIT 5 Transformations in the Coordinate Plane Essential Question: How do we translate a geometric figure in the coordinate plane?
A transformation is a change in a geometric figure’s position, shape, or size. 4 Main Types of Transformations 1.Translations 2.Reflections 3.Rotations 4.Dilations http://nlvm.usu.edu/en/nav/frames_asid_302_g_4_t_ 3.html?open=activities
Translation- a transformation that moves each point of a figure the same distance in the same direction. The shape, size, or orientation does NOT change. So we say the figures are congruent. Polygon- shape made of straight lines and is closed on all sides.
DESCRIBE THE TRANSFORMATION TO THE GREEN HEXAGON THAT WILL PRODUCE THE BLUE HEXAGON.
A dilation is a transformation that changes the size or the shape of a figure but making it larger or smaller. The notation for a dilation is similar to a translation, however, a dilation will always multiply or divide the variables x and y by something. Example (x,y) ----------- (3x+2, y)(x,y) ------------- (2x-3, 3y+1)
Homework: Graph the following figure using the given coordinates. Perform the transformation. Tell whether the transformation is a translation or a dilation. 1) (x,y) ----------- (x-5, y-3)2) (x,y) ----------- (3x+1, 2y) A (1,1)A (-3,1) B (2,1)B (-3,-1) C (1,3)C (-2,1) D (-2,-1) 3) (x,y) ------------ (x+1, y+4)4) (x,y) ----------(2x+1, 3y-3) A (2,-1)A (-1,2) B (1,-2)B (-1,1) C (2,-3)C (0,1) D (3,-2) D (0,2)
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_UIOvEwAhttp://www.youtube.com/watch?v=j1X_UIOvEwA Practice: Reflect the image below as instructed. 1. Reflect over the x-axis2. Reflect over the y-axis
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 1.Point of rotation 2.Angle of rotation 3.Direction of rotation Example: http://www.youtube.com/watch?v=YkQQBH21GiQhttp://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).
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 ̊ = 1 turn 180 ̊ = 2 turns 270˚ = 3 turns clockwise = right counter-clockwise = left 90 ˚ turn clockwise 180˚ turn clockwise 270˚ turn clockwise
Practice 1.rotate 90 ̊ clockwise about the origin2. rotate 90˚ counter-clockwise about the origin 3. rotate 180˚ about the origin4. rotate 270˚ clockwise about the origin
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.
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)
Practice: Describe the transformations that maps the shaded figure onto the non shaded figure. 1. 2. 3.