How Far Between Cities?
Student Page

Part I: Tutorial

You might already have a good understanding of this concept. If as you work through Part I you feel like you already understand the activity, consider skimming it and then go directly to Part II.

After you open the Java Applet please follow these step-by-step directions:

Note: The Java applet will open in a separate window. Arrange your browser windows so that the applet and the student page can be easily viewed.
  1. Select Clear Points (a good habit in case a point had been marked earlier)

  2. Click on the dot on the map indicating the location of Rialto. Use one of the 4 arrows to fine tune the location of the point. The readout in the upper right corner should be x: 196 y: 180

  3. Select Mark Point [Result of this action: nothing visible yet]

  4. Click on the dot on the map indicating the location of Loma Linda. Use one of the 4 arrows to fine tune the location of the point. The readout in the upper-right corner should be x: 402 y: 57

  5. Select Mark Point [Result of this action: a line will appear]

  6. Mark this point x: 196 y: 57. Use one of the 4 arrows to fine tune the location of the point.

  7. Select Mark Point [Result of this action: a second line will appear]

  8. Click on Rialto again. Use one of the 4 arrows to fine tune the location of the point. The readout in the upper right corner should be x: 196 y: 180

  9. Select Mark Point [Result of this action: a third line will appear]

  10. Click in upper-left area of the map. (For example: anywhere northwest of Interstate 15.)

  11. Observe the triangle that has been drawn on your map. It should look something like this:



  12. This is a right triangle. The line segment connecting the locations of the two cities forms the hypotenuse of the right triangle.

  13. What are the coordinates (x, y) of the endpoints of the line segment that is the hypotenuse of the right triangle?

NOTE: As you worked through the guided tutorial, you were prompted to use x and y coordinates that would give you straight vertical or horizontal line segments. As you continue to practice this idea, remember that the side of the triangle parallel to the x axis and the side of the triangle parallel to the y axis should be straight! Attention needs to be given to the x= and y= readout in the upper right corner of the window. If care isn't taken, you won't really have a right triangle.

Practice: Follow similar steps to "draw" two other triangles using the following pairs of cities:

Fontana and San Bernardino
Muscoy and Loma Linda

Assessment:

Generalize the method you used to make a right triangle with any two cities as the endpoints of the hypotenuse. Write the steps needed to have these triangles appear on the map.

Part II:

Now you can apply what you know about right triangles and finding the hypotenuse to the task of calculating the distance between two cities on a map.

Go to Part II

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Selections from Ask Dr. Math Archives:

FAQ: Right Triangle
JavaSketchpad: Drag the red dots and observe the triangle medians, altitudes, and angle bisectors.

Ordered Pairs vs. Coordinates
What is the difference between an ordered pair and coordinates?

Plotting Coordinates on a Graph
How can I solve a problem like 3+(-2) = ? using a number line, and how can I plot coordinates like (-4,3) on an X-Y graph?

A Right Triangle of Points
Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle.

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