Question

If triangle TU'V' represents triangle TUV rotated 90° counterclockwise about the origin, the ordered pair of T' is:

a. (V, -TU)
b. (-V, TU)
c. (-TU, -V)
d. (TU, V)

Answer 1

The ordered pair of T' is (V, -TU). To rotate the point T(x,y) counterclockwise about the origin by 90°, we can use the rotation matrix R = [0 -1] [1 0]. Applying this rotation matrix to the coordinates of T(x,y), we get T'(-y,x).

Step-by-step explanation:

The ordered pair of T' is (V, -TU).

To rotate the point T(x,y) counterclockwise about the origin by 90°, we can use the rotation matrix:

R = [cos(90°) -sin(90°)] [sin(90°) cos(90°)] = [0 -1] [1 0]

Applying this rotation matrix to the coordinates of T(x,y), we get T'(-y,x). So, the ordered pair of T' is (-TU, V).