You've already seen that a position needs an origin and a sign. Someone has to choose where that origin sits and which direction counts as positive.
That pair of choices, a chosen origin plus a chosen positive direction, is called a frame of reference. Positions and motion are measured from it.
Here is one unmoving scene: a school door, a bench 20 m east of it, and a flagpole 25 m east of it. Watch the bench's position as the frame changes. The scene itself never moves.
Four frames, four values, one unmoving bench.
Which two choices define a frame of reference?
A frame of reference uses Maya's front door as the origin, with the direction toward the park counted as positive. Her mailbox stands 9 m from the door, toward the park. Enter the mailbox's position x in meters, including the sign.
The same parked car is recorded at x = +40 m in one frame and at x = -10 m in another. What explains the two values?
A frame of reference puts the origin at a park entrance and counts west as the positive direction. A fountain stands 50 m east of the entrance. Enter the fountain's position x in meters in this frame, including the sign.
Ana measures a statue from the library with east positive and records x = +80 m. Ben measures the same statue from the fountain, also with east positive, and records x = +30 m. Which statement is correct?
In a frame with a school door as the origin and north as the positive direction, a flag stands at x = -15 m. Where is the flag?