An Angle of Rotation Is Specified, Followed by the Coordinates $x ^ { \prime } - y ^ { \prime }$

question 13

Multiple Choice

An angle of rotation is specified, followed by the coordinates of a point in the $x ^ { \prime } - y ^ { \prime }$ system. Find the coordinates of the point with respect to the $x - y$ system. $\theta = 120 ^ { \circ }$ $\left( x ^ { \prime } , y ^ { \prime } \right) = ( \sqrt { 3 } , 8 )$

• A) \(\left( \frac { 5 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)\)
• B) \(\left( - \frac { 9 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)\)
• C) \(\left( - \frac { 5 } { 2 } , - \frac { 9 \sqrt { 3 } } { 2 } \right)\)
• D) \(\left( \frac { 9 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)\)
• E) \(\left( \frac { 9 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)\)

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Definitions:

ASME

American Society of Mechanical Engineers, a professional association that sets codes and standards for engineering practices, especially concerning mechanical engineering.

Threads

The helical structure on a cylindrical object such as a screw or bolt, allowing it to be screwed into a corresponding threaded hole or nut.

Inclined Surface

A surface that slopes or angles away from the horizontal or vertical, often specified in degrees of inclination.

Dimensions

Numerical values given to define the size, shape, or geometric features of a part or assembly in engineering drawings.