We have been given that Y and Z are points on the number line. The length of segment YZ is 9 units and Y lies at -12. We are asked to find the location of point Z.
Since Y and Z are located on number line, so Z can be either on left side of Y or on right side of Y.
When Z is on left side of Y, then we can set an equation as:
[tex]Y-Z=9[/tex]
[tex]-12-Z=9[/tex]
[tex]-12+12-Z=9+12[/tex]
[tex]-Z=21[/tex]
[tex]Z=-21[/tex]
Therefore, the location of Z will be [tex]-21[/tex].
When Z is on right side of Y, then we can set an equation as:
[tex]Z-Y=9[/tex]
[tex]Z-(-12)=9[/tex]
[tex]Z+12=9[/tex]
[tex]Z+12-12=9-12[/tex]
[tex]Z=-3[/tex]
Therefore, the location of Z will be [tex]-3[/tex].
