CPM Homework Help : PC Problem 12-64

Find the image of the line $y = 2 − x$ after a $60°$ counterclockwise rotation about the origin.

Hint:

Review your work from part (a) of problem 12-47.

Step 1:

$( t , 2 - t ) \left[ \begin{array} { c c } { \frac { 1 } { 2 } } & { \frac { \sqrt { 3 } } { 2 } } \\ { - \frac { \sqrt { 3 } } { 2 } } & { \frac { 1 } { 2 } } \end{array} \right]$

Step 2:

$\left. \begin{array} { l } { x = \frac { 1 + \sqrt { 3 } } { 2 } t - \sqrt { 3 } } \\ { y = \frac { \sqrt { 3 } - 1 } { 2 } t + 1 } \end{array} \right.$

Step 3:

Solve for $y$ in terms of $x$ to find the equation of the line after rotation.