12.2 Solving Transformations Problems

Under the three transformations (translation, rotation, reflection) an object and its image are always congruent.

When you reflect a shape on a coordinate grid you have to know the equation of the mirror line. Mirror line is a line that will reflect a shape in front, rear, left, right.

This also important for you to remember:
All vertical lines are parallel to the y-axis and have the equation X = 'a number'
All horizontal lines are parallel to the x-axis and have the equation Y = 'a number'

Here is the example:

When you rotate a shape on a coordinate grid you need to know the coordinates of the centre points, size of haw many degree it turns and the direction whether it's clockwise or anti-clockwise.

When you translate a shape on a coordinate grid, you can describe its movement with a column vector.

This is an example of column vector

 is  

The top number states how many units to move the shape right (positive number) or left (negative number).

The bottom number states how many units to move the shape up (positive number) or down (negative number).

 For example:

 means 'move the shape 2 units left (because it's negative) and 3 units up.