Transformations

Tips for Transformations:

1) Translations - Slides a figure from one location to another.
- You're moving it right or left, and/or up/down.
- If the number is negative, it means it's going to the left or down. If the number is positive, it means it's going right or up.
- When writing coordinates, the first number is the coordinate related to the x axis, and the second number is for the y axis.
               -  (7, 4)  Means it's 7 on the x axis and 4 on the y axis.
               - Both numbers are positive, so it would be to the right 7                   units and up 4 units.

2) Reflections - Reflects a figure in a mirror line to create a congruent image.

- You count how many squares a point is from the mirror line, then to reflect it, you count the same number to the other side to find your point. You did this for all points (vertices).
- A problem could say reflect over the horizontal/vertical mirror line or it could say x = a number, y = a number.

- For example: Reflection in a horizontal mirror line through (0, 5). If the mirror line is not drawn for you, you would draw a line horizontally through point (0,5). Horizontal lines correspond to the y axis.  
- A horizontal reflection is through the y axis.
- A vertical reflection goes through the x axis.
** Do not confuse this with the x axis going vertically and the y axis going horizontally.

3) Rotations: A figure is turned about a fixed point, called the turn centre. 
- You can rotate the shape clockwise (CW) or counter-clockwise (CCW).
- CW is to the right.  CCW is to the left.
- You can rotate the shape 90 degrees, 180 degrees, or 270 degrees 
(you probably won't see the 270 degrees turn though this year)
- 90 degrees is 1/4 turn.
- 180 degrees is 1/2 turn.
- 270 degrees is 3/4 turn.

- When completing a rotation, you're placing your pencil on a specific point. The point can be one of the vertices of the shape, in the shape, or outside the shape. It could be anywhere.

Steps to rotate a shape:
1) If the shape is not already drawn on the grid paper, you draw it on the grid paper.

2) Place tissue paper on top of the shape/grid and trace the shape onto the tissue paper.

3) Place a little arrow at the top so you know which direction you started from. Line the arrow up with one of the grid lines. It doesn't really matter where you place the arrow, it's just there so you can keep track of how much you have turned the tissue paper.

4) Place your pencil on the point you're told to rotate it. 

5) Slowly turn the tissue paper in which ever direction the question asks; either CW or CCW.

6) When you see the arrow finish the 90, 180, or 270 degree turn, you have completed your rotation.

7) Draw the new image onto your grid paper. Keeping your pencil on one of the vertices of the new image, slide the tissue paper out and plot one point. Do this for all points.

8) Once you've plotted all points of the rotated image, then connect your dots to close the shape.

9) Label all points. Remember to place the "prime" symbol after transforming your image. This is the prime symbol ('). 

For example: Rotate the figure 90 degrees CW about point (3,4).
- This means you rotate the shape 1/4 turn to the right at the point 3,4. (X = 3, Y =4).

Other:

- Don't forget to label all points.
- Place the prime symbol (') after a transformation. If you complete 2 transformations, the labels would have 2 prime symbols (''), if it's the 3rd transformation, the labels would have 3 prime symbols (''') and so on.- The more you practise, the easier it will be. :) :) :)