Question

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

If YZ = 9 and Y lies at -12 , where could Z be located?

If there is more than one location, separate them with commas.

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`.