Squashed How many times must the transformation given by the matrix

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Presentation transcript:

Squashed How many times must the transformation given by the matrix be applied to the quadrilateral so that the resultant quadrilateral is inside the circle shown.

Squashed How many times must the transformation given by the matrix be applied to the quadrilateral so that the resultant quadrilateral is inside the circle shown. Notes and Solution The point (2,6) is furthest from the origin, a distance of √40. 6 < √40 < 7 and so applying transformation (an enlargement with scale factor ½) twice gives an image a distance within 7/4 from the origin. Applying the transformation only once gives an image a distance greater than 3 from the origin. Therefore the answer is twice.

Identity crisis Calculate

Identity crisis Calculate Notes and Solution The matrix is an anticlockwise rotation by 73° about the origin. From this diagram it’s clear that the point (cos 17°, sin 17°) moves to (0, 1) when this transformation is applied. The answer is therefore