A position answers two questions: how far across, and how far up? Move the point using its coordinates before we ask it to travel.
Drag in the picture or use the labelled inputs and sliders. Grid squares span 25 world units. This is a mathematical model running in your browser.
Choose an origin
The crossing of the axes is our origin: (0, 0). Coordinates are written (x, y), with the horizontal value first. A point at (120, 90) lies 120 units right of the origin and 90 units above it. These are world units; resizing the picture does not change the point’s position.
Make X negative while leaving Y at 90. The point crosses to the left, but stays at the same height. Now make Y negative too. The signs tell us which side of each axis contains the point.
Position and movement
A position is where something is. A displacement is the change from one position to another. To get from (20, 30) to (120, 90), subtract start from finish: Δx = 120 − 20 = 100 and Δy = 90 − 30 = 60. The symbol Δ means “change in”.
From (120, 90), move 30 units left and 50 units down. Where will the point end up?
Show the explanation
(90, 40): add −30 to X and −50 to Y. A negative change does not necessarily produce a negative position.
Set that result using the controls. If a point moves in the wrong direction, check the coordinate order and the signs. Many screen APIs count Y downwards; this experiment keeps world Y upwards and reverses it only when drawing.