To determine the possible coordinates of point [tex]\( G \)[/tex] on a number line, we start with point [tex]\( E \)[/tex] having a coordinate of [tex]\(-4\)[/tex] and the distance [tex]\( E G \)[/tex] given as [tex]\( 5 \)[/tex]. This means point [tex]\( G \)[/tex] is 5 units away from point [tex]\( E \)[/tex].
Since the distance on a number line can be in either direction (to the right or to the left), we need to consider both possibilities.
1. Move to the right:
If we move 5 units to the right of [tex]\(-4\)[/tex], we can find the coordinate of [tex]\( G \)[/tex] by adding 5 to [tex]\(-4\)[/tex]:
[tex]\[
G_1 = -4 + 5 = 1
\][/tex]
2. Move to the left:
Alternatively, if we move 5 units to the left of [tex]\(-4\)[/tex], we can find the coordinate of [tex]\( G \)[/tex] by subtracting 5 from [tex]\(-4\)[/tex]:
[tex]\[
G_2 = -4 - 5 = -9
\][/tex]
So, the possible coordinates of point [tex]\( G \)[/tex] are [tex]\( 1 \)[/tex] and [tex]\(-9\)[/tex].
Hence, the coordinates of point [tex]\( G \)[/tex] can be [tex]\( 1 \)[/tex] or [tex]\(-9\)[/tex].
