Question

Identify the matrix transformation of TUV, which has the coordinates T(0,1) U(1,2) V(2,0), for 90° rotation, clockwise. Then identify the correct vertices of the image.

Answer 1

Answer:

[0 1][ 0 1 2] = [1 2 0]

[-1 0][ 1 2 0] [0 -1 -2]

T'(1, 0), U'(2, 1), W'(0, -2)

Explanation:

The rule to rotate a figure 90 degrees clockwise about a point is

(x, y) --> (y, -x)

It means that we need to interchange x and y and then, the second coordinate will have the opposite sign.

To interchange the coordinates, we use the following matrix

[ 0 1 ]

[ 1 0 ]

Then, the second coordinate has the opposite sign, so the second row will have the opposite sign

[0 1 ]

[-1 0 ]

Therefore, the matrix for a 90 degrees rotation clockwise is

[0 1 ]

[-1 0 ]

And the answer is

[0 1][ 0 1 2] = [1 2 0]

[-1 0][ 1 2 0] [0 -1 -2]

Where each column of the second matrix are the coordinates of T, U, and V. Then, the new vertices of the figure will be

T'(1, 0) U'(2, 1) W'(0, -2)