To find the location of point [tex]\(D\)[/tex] on the number line, we can use the midpoint formula. The midpoint [tex]\(E\)[/tex] of a segment [tex]\(\overline{CD}\)[/tex] is given by:
[tex]\[ E = \frac{C + D}{2} \][/tex]
Given:
- [tex]\( C = 8 \)[/tex]
- [tex]\( E = -3 \)[/tex]
We can plug these values into the midpoint formula and solve for [tex]\(D\)[/tex]:
[tex]\[ -3 = \frac{8 + D}{2} \][/tex]
To eliminate the fraction, multiply both sides by 2:
[tex]\[ 2 \times (-3) = 2 \times \left(\frac{8 + D}{2}\right) \][/tex]
[tex]\[ -6 = 8 + D \][/tex]
Next, isolate [tex]\(D\)[/tex] by subtracting 8 from both sides:
[tex]\[ -6 - 8 = D \][/tex]
[tex]\[ -14 = D \][/tex]
Therefore, point [tex]\(D\)[/tex] is at [tex]\(-14\)[/tex] on the number line.
So from the drop-down menu, we select [tex]\(\boxed{-14}\)[/tex].
