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On a number line, point [tex]C[/tex] is at 8, and the midpoint [tex]E[/tex] of [tex]\overline{CD}[/tex] is at -3.

Point [tex]D[/tex] is at [tex]\square[/tex] on the number line.

A. [tex]-14[/tex]
B. [tex]2[/tex]
C. [tex]-2[/tex]
D. [tex]19[/tex]

Sagot :

GinnyAnswer
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].
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