12.2 Solving Transformation Problems

When a shape undergoes any of these three transformations it only changes its position. Its shape and size stay the same. Under these three transformations, an object and its image are always congruent.

When you reflect a shape on a coordinate grid you need to know the equation of the mirror line.

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’

Some examples are shown on the grid on the right.

When you rotate a shape on a coordinate grid you need to know the coordinates of the centre of rotation, and the size and direction of the turn.

When you translate an example of a column vector: 4,5

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

For example: 

(4,5) means : ‘move the shape 4 units right and 5 units up’

(-2,-3) means: ‘move the shape 2 units left and 3 units down’

You can see any these three transformations to solve all sorts of problem