Starter Fill in all the blank boxes

Combinations of Transformations Lesson 5 Aim: To be able to find a single matrix to describe a combination of transformations.

Combinations We can find a s__________ transformation matrix that performs two transformations. This is done by m________________ the two matrix transformations. The o_______ you multiply depends on the order you want to apply the transformations in. This may not matter but quite often does. Transformation Matrix B is applied second. Transformation Matrix A is applied first. B multiplied by A will give you the transformation matrix that performs both transformations in one go.

Combination Transformations Example 1 Find the matrix that represents an enlargement, centre O, scale factor 2 followed by a rotation, centre O, anticlockwise through 900. May find useful Rotation θ0 Anticlockwise about (0,0)

Rotation θ0 Anticlockwise On w/b Find the matrix that represents an enlargement, centre O, scale factor 1/2 followed by a rotation, centre O, anticlockwise through 450. May find useful Rotation θ0 Anticlockwise about (0,0)

Combination Transformations Example 2 Find the matrix representing a reflection in the line y = x followed by a stretch scale factor 3 parallel to the x-axis. May find useful Reflection in y=xtanθ

On w/b Reflection in y=xtanθ May find useful Find the matrix representing a reflection in the line y = -x followed by a stretch scale factor 2 parallel to the y-axis. May find useful Try Exercise 4D page 48 Be careful with the order you apply them in. Also try to consider if you would get the same result if the order was reversed. Reflection in y=xtanθ

Extension Matrix Determinant The determinant of a 2 x 2 matrix M = is defined as ad - bc It is denoted as det M or M Example find the determinants of these:

Determinant – interesting! What type of transformation do all of these set of matrices perform? Work out each of their determinates and state what you find. All determinants equal ___ when the transformation is s___________ and a r____________.

Determinant – interesting!! What type of transformation do all of these set of matrices perform? Work out each of their determinates and state what you find. All determinants equal ___ when the transformation is s___________ and a r____________.

Determinant – interesting!!! What type of transformation do all of these set of matrices perform? Work out each of their determinates and state what you find. These transformations are all s____________ and the determinant tells us the ________ of the a_____ e_____________ Transformed by matrix A gives