Question

Suppose that Y and Z are points on the number line.

Answer 1

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:

$Y-Z=9$

$-12-Z=9$

$-12+12-Z=9+12$

$-Z=21$

$Z=-21$

Therefore, the location of Z will be $-21$.

When Z is on right side of Y, then we can set an equation as:

$Z-Y=9$

$Z-(-12)=9$

$Z+12=9$

$Z+12-12=9-12$

$Z=-3$

Therefore, the location of Z will be $-3$.