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On a number line, point A has a coordinate of −6, and point B has a coordinate of 2. Which is the coordinate of point M, the midpoint of AB?


A:4

B:−2

C:0

D:−3

Respuesta :

cerverusdante
To solve this, we just need to find the distance between the points A and B in the number line, and then, divide that distance by 2.
Remember that the distance formula between tow point in the number line is: 
[tex]d=|x_{2}-x_{1}|[/tex]
From our point we can infer that [tex]x_{1}=-6[/tex] and [tex]x_{2}=2[/tex], so lets replace the values:
[tex]d=|x_{2}-x_{1}|[/tex]
[tex]d=|2-(-6)|[/tex]
[tex]d=|2+6|[/tex]
[tex]d=8[/tex]

Now, to find the coordinate of the midpoint, we just need to divide that distance by 2:
[tex]M= \frac{8}{2} [/tex]
[tex]M=4[/tex]

We can conclude that the coordinate of the point M, the midpoint of AB, is 4

Answer:

The correct option is B.

Step-by-step explanation:

It is given that on a number line, point A has a coordinate of −6, and point B has a coordinate of 2. It means

[tex]x_1=-6[/tex]

[tex]x_2=2[/tex]

Midpoint formula:

[tex]x=\frac{x_1+x_2}{2}[/tex]

[tex]x=\frac{-6+2}{2}[/tex]

[tex]x=\frac{-4}{2}[/tex]

[tex]x=-2[/tex]

The coordinate of point M is -2. Therefore option B is correct.

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