To determine the locations of points [tex]\( R \)[/tex] and [tex]\( S \)[/tex] given that they are each 6 units away from point [tex]\( Q \)[/tex], which is located at [tex]\(-14\)[/tex], we follow these steps:
1. Finding Point [tex]\( R \)[/tex]:
Point [tex]\( R \)[/tex] is located 6 units to the right of point [tex]\( Q \)[/tex]. When we move to the right (increasing direction on the number line), we add the distance to the position of [tex]\( Q \)[/tex].
- The original position of [tex]\( Q \)[/tex] is [tex]\(-14\)[/tex].
- Adding the distance of 6 units:
[tex]\[
R = -14 + 6 = -8
\][/tex]
2. Finding Point [tex]\( S \)[/tex]:
Point [tex]\( S \)[/tex] is located 6 units to the left of point [tex]\( Q \)[/tex]. Moving to the left (decreasing direction on the number line), we subtract the distance from the position of [tex]\( Q \)[/tex].
- The original position of [tex]\( Q \)[/tex] is [tex]\(-14\)[/tex].
- Subtracting the distance of 6 units:
[tex]\[
S = -14 - 6 = -20
\][/tex]
So, the coordinates for points [tex]\( R \)[/tex] and [tex]\( S \)[/tex] are:
[tex]\[
R = -8
\][/tex]
[tex]\[
S = -20
\][/tex]
Thus, points [tex]\( R \)[/tex] and [tex]\( S \)[/tex] are located at [tex]\(-8\)[/tex] and [tex]\(-20\)[/tex], respectively.
