Coordinate Plane: Distance Formula - Pythagorean Theorem
In the plane below, you can move the BIG BLACK POINTS anywhere you'd like. Observing the two points relationship by click the "Hint" box.
2-1: In the plane above, what do you notice?
2-2: How can you calculate the length of the green segment, or |RISE|, WITHOUT counting spaces (or gridlines)?
2-3: How can you calculate the length of the red segment, or |RUN|, WITHOUT counting spaces (or gridlines)?
2-4: Let's call "d" the distance between point A and point B. Write an equation that expresses the relationship among d, |RISE|, and|RUN|.
2-5: STUDENTS:For the two ordered pairs (x, y) displayed, calculate the following:
1) Absolute value of the RISE between those two points
2) Absolute value of the RUN between those two points
Then,
3) Use the Pythagorean Theorem to determine the distance between both points.
Enter an EXACT ANSWER in the Exact Distance input box.
For any value you enter correctly, this GeoGebra applet will tell you if it is right or not.
2-6: For help visualizing the right triangle formed, see the below GeoGebra applet. You can reposition the 2 LARGE POINTS anywhere you'd like!