Question

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

Answer 1

The correct option is B.

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

`x_1=-6`

`x_2=2`

Midpoint formula:

`x=(x_1+x_2)/(2)`

`x=(-6+2)/(2)`

`x=(-4)/(2)`

`x=-2`

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

Answer 2

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:

`d=|x_(2)-x_(1)|`
From our point we can infer that
`x_(1)=-6` and
`x_(2)=2`, so lets replace the values:

`d=|x_(2)-x_(1)|`

`d=|2-(-6)|`

`d=|2+6|`

`d=8`

Now, to find the coordinate of the midpoint, we just need to divide that distance by 2:

`M= (8)/(2)`

`M=4`

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