TRANSFORMATIONS
To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include: TRANSLATION ROTATION REFLECTION
TRANSFORMATIONS Translation Rotation Reflection
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
TRANSLATION – MOVE FROM ONE POINT TO ANOTHER REFLECTION, ROTATION, OR TRANSLATION TRANSLATION – MOVE FROM ONE POINT TO ANOTHER Translation
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION
REFLECTION, ROTATION, OR TRANSLATION Reflection in multiple mirrors. Reflection in multiple mirrors.
Let's examine some translations related to coordinate geometry. Translations are SLIDES!!! Let's examine some translations related to coordinate geometry.
TRANSLATION: 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, C Label 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)
Count the number of horizontal units the image has shifted. Count the number of vertical units the image has shifted. We would say the Transformation is: 1 unit left,6 units up or (-1+,6)
What 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?
A 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
WRITE THE POINTS What are the coordinates for A, B, C? How did the transformation change the points?
What is the translation shown in this picture? 6 units right, 5 units up or (+6,+5)
LET´S DO IT TOGETHER Draw a trapezoid with vertices (-5, -2), (-1, 3), (-1, -5), and (-5, -6). Then move it 6 units right. What are the new coordinates?
a. The new coordinates are (1, -2), (5, 3), (5, -5), and (1, -6).
REFLECTIONS
REFLECTIONS Is 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.
Reflect the figure across the x-axis. Course 2 Reflect 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.
A 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.
REFLECTING OVER THE Y-AXIS: Where do you think this picture will end up?
REFLECTION The coordinates of A'B'C'D'E'F'G'H' are: A’(+2,+2)
LET´S DO IT TOGETHER Draw 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?
The new coordinates are (2, -8), (1, -8), (1, 8), and (2, 8).
ROTATION: A turn about a fixed point called “the center of rotation” The rotation can be clockwise or counterclockwise
ROTATION: A turn about a fixed point called “the center of rotation” The rotation can be clockwise or counterclockwise.
ROTATIONS The 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.
LET´S DO IT TOGETHER Rotate 90 clockwise about (0, 0).
Rotate 90° clockwise about (0, 0).
YOUR TURN Rotate. Translate and reflect this figure.