A rotation is when you turn a shape using a specific angle measurement and direction around a certain point. The angle measurement used is the angle of rotation. We will be working with specific degrees of rotation, which we should have an understanding of what these look like from the previous unit on angles. The point that the shape is being rotated around is the point of rotation, and the direction (clockwise or counterclockwise) is the direction of rotation.
We have noted some real life examples of rotations and their centers of rotation during class.
Notice in the example below that the center of rotation that is used is also a point on the shape. This can be the case, or the shape may be rotated around the origin.
A translation is when something moves to a new position through lateral moves (up, down, left, right). Every point will move the same distance in the same direction, just as in a reflection, except a translation does not require a line of reflection. It is simply sliding a shape in a specific direction. This is another form of a rigid transformation, as the shape did not change in size. Any rigid transformation will result in isometry because the distance between the points does not change so they are still the same. If all new points have an equal distance as they did with the original points, it is isometry.
Brief Review Activity - Use paper cut in the shape of the image being reflected and literally flip it over the line of reflection (specifically the x or y-axis). Notice that the coordinate that stays the same is the same as the axis of reflection, while the other coordinate changes to its opposite in sign.
When thinking of a reflection, remember that it is the opposite of what is happening, which can help as a reminder to which coordinates should change. The shape of the image stays the same, and it is only moving in position so this is a type of rigid transformation.
Project will assess understanding of the four types of transformations.
It was provided on 3/23 and is due on 4/15 at the end of the unit.
1) Explain the shift if you add three to the x coordinate and subtract 1 from the y coordinate. What type of transformation is this? Would this image remain congruent to the pre-image?
2) The original coordinates of a triangle are (1,1) (4,1) (4,5). The new coordinates are (1, -1) (4, -1) and (4,-5). What happened to this triangle? What type of transformation took place and how do you know?
3) Explain how the coordinates change in a 90 degree counterclockwise rotation. What stays the same?
4) When a figure is dilated by a factor of 3 how do the coordinates change. Is your new figure still congruent if not, explain the relationship between the two.