22REFLECTION, ROTATION, OR TRANSLATION Reflection in multiple mirrors.Reflection in multiple mirrors.
23Let's examine some translations related to coordinate geometry. Translations are SLIDES!!!Let's examine some translations related to coordinate geometry.
24TRANSLATION: A slide along a straight line. Count the number of horizontal units and vertical units represented by the translation arrow.Label the vertices A, B, CLabel the new translation A’, B’, C’The horizontal distance is 8 units to the right, and the vertical distance is 2 units down(+8 -2)
25Count the number of horizontal units the image has shifted. Count the number of vertical units the image has shifted.We would say theTransformation is:1 unit left,6 units up or(-1+,6)
26What about the other letters? In this example we have moved each vertex 6 units along a straight line. If you have noticed the corresponding A is now labeled A’What about the other letters?
27A TRANSLATION"slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction
28WRITE THE POINTS What are the coordinates for A, B, C? How did the transformation change the points?
29What is the translation shown in this picture? 6 units right, 5 units up or(+6,+5)
30LET´S DO IT TOGETHERDraw a trapezoid with vertices (-5, -2), (-1, 3), (-1, -5), and (-5, -6). Then move it 6 units right. What are the new coordinates?
31a. The new coordinates are (1, -2), (5, 3), (5, -5), and (1, -6).
33REFLECTIONSIs figure A’B’C’D’ a reflection image of figure ABCD in the line of reflection, n?How do you know?Figure A'B'C'D' IS a reflection image of figure ABCD in the line of reflection, n.Each vertex in the red figure is the same distance from the line of reflection, n, as its reflected vertex in the blue image.
34Reflect the figure across the x-axis. Course 2Reflect the figure across the x-axis.The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites.
35A reflection is often called a flip A reflection is often called a flip. Under a reflection, the figure does not change size. It is simply flipped over the line of reflection.Reflecting over the x-axis:When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.
36REFLECTING OVER THE Y-AXIS: Where do you think this picture will end up?
37REFLECTION The coordinates of A'B'C'D'E'F'G'H' are: A’(+2,+2)
38LET´S DO IT TOGETHERDraw a rectangle with vertices (-2, -8), (-1, -8), (-1, 8), and (-2, 8). Then reflect it in the y-axis. What are the coordinates of the reflected shape?
39The new coordinates are (2, -8), (1, -8), (1, 8), and (2, 8).
40ROTATION: A turn about a fixed point called “the center of rotation” The rotation can be clockwise or counterclockwise
41ROTATION: A turn about a fixed point called “the center of rotation” The rotation can be clockwise or counterclockwise.
42ROTATIONSThe coordinates for the centre of rotation are (–4, –4). b) Rotating the figure 90° clockwise will produce the same image as rotating it 270° in the opposite direction, or counterclockwise.
43LET´S DO IT TOGETHERRotate 90clockwise about (0, 0).