9DH August 2006 Rotation about a given point. & Writing the coordinates of the images. & Learning about how to draw the x and y axis. & Making mathematical observations

9DH August 2006 Making mathematical observations. If this is ‘easy’ for you then your job is thinking about how you are going to TEACH your class mates how to do this – and your instructions can be added to the end of the powerpoint.

Today is our last lesson on this task… By the end of this lesson you should beable to rotate a given shape (or image) about the given point of rotation. ¼ turns (90degrees), ½ turns (180degrees) and ¾ turns (270degrees) in a clockwise OR anticlockwise direction Label the image points correctly and state the coordinates.

Task: Use a whole page Put the point (0,0) in the middle of your page. Draw the x and y axis. (remember the y hangs down.) Label the x and y axis, right to the edge of the page. Remember where the negatives go! Draw the following points, label them, join them together with straight lines to form a polygon. Point A(3,4); Point B(5,6); Point C(7,2) Rotate the triangle a quarter turn clockwise about the point (0,0) and label the points A’, B’ and C’ To the right of the image list the points and their coordinates.

The triangle looks something like this.

And after the rotation ¼ turn clockwise about (0,0).

On the same page. Point A(3,4); Point B(5,6); Point C(7,2) (the SAME triangle) Rotate the triangle a half turn clockwise about the point (0,0) and label the points A’’, B’’ and C’’ To the left of the image list the points and their coordinates. Write “triangle ABC rotated half a turn about (0,0)” below the triangle.

WHAT can you notice about the co-ordinates? Can you spot a pattern? Can you write down the pattern in a mathematical statement? Words that might help: Left, right, up, down Squares Hint: look at (3,4) (3,-4) (-4,-3) and (-4,3) What do these points have in common?

9DH: Learnt