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Coordinate Plane: Distance Visualization

In this activity, we are going to explore the movement of the two points on the coordinator plane. You could move the two black points anywhere and test the movement between the two points. Press MOVE. Then CONTINUE.

What do you notice? What do you wonder?

In this app, position the two points to create a right triangle whose legs measure 5 units and 8 units.

Here, place the runner's initial point at (1,-4). Place the other point at (-5,3). Then press the buttons (like before) to create a right triangle.

Based on the above activities, what do you notice about distance "d"?

What method or concept could you use to find the distance "d"? What is the related formula?