PRESENTATION OUTLINE
TRANSFORMATION ASSESSMENT
TRANSLATIONS
A translation slides a figure in a certain direction, usually according to a line vector. It does not change anything about the angles, line lenghts, parallel lines, or the shape of the figure. The only thing that changes are the coordinates, if it's on a coordinate plane, because if it's a translation it will move from its original spot. It is possible to give ending cooridinates of an image without drawing the translation. For example, if a pre-image is located 5 units right of an image, you can subtract 5 from the given point.
While performing a translation, it is important to remember that every vertex must move the same distance as the others. The figure goes 6 units down and 3 units right.
ROTATIONS
A rotation turns a figure based on a given direction and degree. A figure will either turn 90, 180, 270, or 360 degrees , positive or negative. If you are directed to rotate positive, you turn the figure counter-clockwise. If you are directed to rotate negative, you turn the figure clockwise. Angles, line lengths, parallel lines, and shapes do not change during a rotation. However, like a translation, coordinates do change. This is because it moves to a different part of the coordinate plane. If you replicate a pre-image but in a different quadrant, you won't have to use a coordinate plane.
While rotating a figure, make sure you correctly label the images with an ' (prime sign) as seen above. Rotations can get complicated if you don't label the pre-image as well. Every time you rotate you need to add a prime sign to each point. In the picture above, the figure turns -90 degrees.
REFLECTION
A reflection is done by flipping a figure over a line of reflection. The image will always appear symmetrical to the pre-image. The angles, line lengths, parallel lines, and the shape of the figure do not change during a reflection. The coordinates will change though. If the line of reflection is on an axis, you do not have to use a coordinate plane to get ending coordinates. This is because the numbers will stay the same, but their signs (+/-) will change.
When directed to make a reflection, keep in mind that the line of reflection won't always be the Y or X axis. If the line of reflection is verticle, call it y= (# line goes through). If it's horizantal, call it x= (# line goes through). In the example above, the line of reflection is the x-axis.
DILATIONS
A dilation is when a figure grows or shrinks, but keeps the same overall shape. In order to successfully dilate a figure, you must know the scale factor and the where the center of dilation is. Angles, parallel lines, and the shape of the figure always stay the same after a dilation. The lengths of the lines will reduce and/or enlarge based on the scale factor of the dilation. The coordinates will also change (if done on a coordinate plane, it does not have to be) because the size is changing. If you have a scale factor of 3, you can multiply all of the coordinates by 3, and that will give you the coordinates to the image. That way you don't have to use a coordinate plane while making a dilation
Precision is KEY while making a
dilation! Do not forget that if your lines aren't straight, your outcome may not be accurate/correct. Certain scale factors shrink and dilate figures. If the scale factor is negative it flips over the original figure. If it's less than 1 it shrinks, and if it's greater than one it enlarges. Finally, if the scalw factor is 1, the figure stays the same.
