Question

Reason quantitatively. On a number line, the coordinate of point A is negative and the coordinate of point B is positive. a. When will the midpoint of line AB be positive?b. when will the midpoint of line AB be negative? c. when will the midpoint of line AB be zero?d. when will the distance from A to B be negative?

Answer 1

On a number line, the coordinate of point A is negative and the coordinate of point B is positive.

The mid point is defined as:

`M=(A+B)/(2)`

a. When will the midpoint of line AB be positive?

When B>A

b. when will the midpoint of line AB be negative?

When A>B

c. when will the midpoint of line AB be zero?

When:

`\left|A\right|=\left|B\right|`

d. when will the distance from A to B be negative?

Never the distance is not defined as negative by definition of distance.

The distance is a magnitude and for this reason not makes sense say negative distance because is always 0 or positive, if for example we find the distance from A to A is 0 since we are in the same point, but we never say we travel -200 m to reach a city for example.