Question

home work check FAN MEDAL AND TESTIMONIAL

An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?

Z(-3, -7)
Z(7, 3) <------
Z(-7, -3)
Z(7, -3)

Answer 1

Incorrect. If you're familiar with linear algebra and the rotation matrix (I think you should be, given this question), try it out. Apply the rotation matrix to the given vector and see what you get out.

\[\left[\begin{matrix}\cos(180) & -\sin(180) \\ \sin(180) & \cos(180) ?\end{matrix}\right]\left(\begin{matrix}7 \\ 3\end{matrix}\right) = ?\]

Answer 2

To see the answer we want, we can rotate the point back to the original point. That is, we can take the image vector and rotate by -180 degrees.

Note, these happen to be the same thing. Rotating by 180 is the same as rotating by -180.

Answer 3

Thank You!