Question

A bicycle wheel is represented in a coordinate plane with the center of the wheel at the origin. Reflectors are placed on the bicycle wheel at points $(7,4)$ and $(-5,-6)$. After a bike ride, the reflectors have rotated $90°$ counterclockwise about the origin. What are the locations of the reflectors at the end of the bike ride?

Answer 1

Find the locations of the reflectors of the bike ride.

As we have given reflectors are placed on the bicycle wheel at points $\mathrm{A}(7,4)$ and $\mathrm{B}(-5,-6)$.

Since, we know that rotation of $90°$ counterclockwise about the origin then coordinates changes as:

$\mathrm{P}(\mathrm{x},\mathrm{y})=\mathrm{P}\text{'}(-\mathrm{y},\mathrm{x})$

Using the above criteria of rotation of $90°$ counterclockwise about the origin new coordinates are:

$$\begin{gathered} \mathrm{A}(7,4)=\mathrm{A}\text{'}(-4,7) \\ \mathrm{B}(-5,-6)=\mathrm{B}\text{'}(6,-5) \end{gathered}$$

Hence, the new coordinates of the reflectors are $\mathrm{A}\text{'}(-4,7)$ and $\mathrm{B}\text{'}(6,-5)$.