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Question 4:

Give an example of a 2 by 2 rotation matrix that rotates the point
( 4 , 5 )
into the square with corners
( -3 , -7 )
( -1 , -7 )
( -1 , -5 )
( -3 , -5 )

You will probably need to experiment to find a suitable rotation. You can check that your answer works correctly by applying your matrix to the point above. The diagram below shows the location of the point (small blue triangle) and the square (red) - but you may find it useful to draw your own diagram on paper.

Your answer to Question 4:

Q4 square coords
-3 -7
-1 -7
-1 -5
-3 -5
-3 -7

Q4 point
4 5

Question 5:

The final image point ( 8.725 , 7.316 )
is the result of taking an initial point with coordinates (u,v)
reflecting it in the line y = -3x + 3
then rotating it by 60 degrees about point ( 3 , 3 )

What are the values of u and v?
It is strongly recommended that you check your working by plotting the points involved.

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Solution Summary

Give an example of a 2 by 2 rotation matrix that rotates the point (4,5) into the square with
corners (-3, -7), (-1, -7), (-1, -5), and (-3, -5)

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Question 4:
Give an example of a 2 by 2 rotation matrix that rotates the point (4,5) into the square with corners (3, 7), (1, 7), (1, 5), and (3, 5)

Solution: Trying different angles, we find that rotating the point by 200º or radians will move the point inside the square close to its center at The rotation is shown below.
So the 2 by 2 rotation matrix is

Then

Question ...

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