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Q: When is a point between two other points?

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They must be collinear.

Twice the distance between a point and halfway to the other point.

The halfway point between two other defined points.

Do you mean "Between two other points? If yes, when it lies on a straight line between both points that are farther away and on the same line.

Length or distance between two points.

since you know of one points and the halfway point between the other point. just multiply the halfway point by 2 and this is the total distance between the two points.

It is the midpoint

a line segment is not a point but a series of points between two definite end points

Then one point is 20 units away from the other.

It is a line segment.

a point intermediate to two other points, (as in between the hills) a form of restriction (between you and me) indicating two or more alternatives (a choice between going or staying)

a line.

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