Hello, Joanne!
Did you make a sketch?
If a circle with its centre at the origin has a chord with slope $\displaystyle m$,
the equation of the right bisector of the chord is: $\displaystyle y \,=\,mx$
Is this statement true or false? . . . . false Code:
A 
o * *
* * *
*  * *
*  * *
 * *
*  * * *
  *     *     o  
*  * B

*  *
*  *
*  *
* * *

Chord $\displaystyle AB $ has slope $\displaystyle m.$
The perpendicular bisector of the chord does pass through the origin,
. . but its slope is $\displaystyle \frac{1}{m}$
Its equation is: .$\displaystyle y \:=\:\frac{1}{m}\,y$