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.
[b][size=150]2-1: In the plane above, what do you notice?[/size][/b]
[size=150][b][color=#38761d]2-2: How can you calculate the length of the green segment, or |RISE|, WITHOUT counting spaces (or gridlines)? [br][/color][/b][/size][br]
[color=#cc0000][b][size=150]2-3: How can you calculate the length of the red segment, or |RUN|, WITHOUT counting spaces (or gridlines)? [/size][/b][/color]
[size=150][b][color=#000000]2-4: Let's call "[i]d[/i]" the distance between point [i]A[/i] and point [i]B[/i]. Write an equation that expresses the relationship among [i]d[/i], [/color][color=#38761d]|RISE|[/color][color=#000000], and[/color][color=#cc0000]|RUN|[/color][color=#000000].[/color][/b][/size][br]
[b][size=150]2-5: STUDENTS:For the two ordered pairs (x, y) displayed, calculate the following:[br][br][color=#9900ff]1) Absolute value of the RISE between those two points[/color][br][br][color=#0000ff]2) Absolute value of the RUN between those two points[/color][br][br]Then,[br][br]3) Use the Pythagorean Theorem to determine the distance between both points. [br] Enter an EXACT ANSWER in the Exact Distance input box. [br] [br]For any value you enter correctly, this GeoGebra applet will tell you if it is right or not. [/size][/b]
[b][size=150]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! [/size][/b]
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Information: Coordinate Plane: Distance Formula - Pythagorean Theorem