Answered

Connect with a global community of knowledgeable individuals on IDNLearn.com. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

Select the correct answer from the drop-down menu.

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 :

GinnyAnsweridn
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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.