Coordinate of ?ABCD is WCS are: lowermost corner A(2,2) & diagonal corner are C(8,6). W.r.t MCS. The coordinates of origin of WCS system are (5,4). If the axes of WCS are at 600 in CCW w.r.t. the axes of MCS. Find new vertices of point A in MCS.
A)(4.268, 6.732)
B)(5.268, 6.732)
C)(4.268, 4.732)
D)(6.268, 4.732)

Question

Quizplus · Accepted Answer

To find the new coordinates of point A in the Main Coordinate System (MCS), we first translate the WCS origin to the MCS origin, then rotate the point A's coordinates accordingly. Given the WCS origin is at (5,4) in MCS and the rotation is 60 degrees counterclockwise, we apply rotation matrix to point A's WCS coordinates (2,2) after translating them relative to the MCS origin. The rotation matrix for 60 degrees is $\begin{bmatrix} \cos(60^\circ) & -\sin(60^\circ) \ \sin(60^\circ) & \cos(60^\circ) \end{bmatrix}$ = $\begin{bmatrix} 0.5 & -\sqrt{3}/2 \ \sqrt{3}/2 & 0.5 \end{bmatrix}$. After applying the rotation and translation, the new coordinates are approximately (4.268, 6.732).

Coordinate of ?ABCD Is WCS Are: Lowermost Corner A(2,2)