Activity: How can you find the distance (in miles) between Rialto and Loma Linda using this map?
Note: If you need more review about how the triangles are important, you can review Part I again.
To look at the map, Open the Java Applet
Note: It will open in a separate window. Arrange your browser windows so that the applet and the student page can be easily viewed.
Here are some things to notice on the map:
- display of x (in pixels)
- display of y (in pixels)
- scale of pixels to miles
NOTE: A pixel is the basic unit of the composition of an image on a computer monitor (usually a single-colored dot).
Assuming that care has been taken to have horizontal and vertical line segments, here are some questions to think about:
Looking at the x-coordinates
Looking at the y-coordinates
- Click on Rialto. What value is x?
- Click on Loma Linda. What value is x?
- What is the difference between the two values of x?
Suppose we drew some lines on the map:
- Click on Rialto. What value is y?
- Click on Loma Linda. What value is y?
- What is the difference between the two values of y?
- Does the horizontal line segment represent the difference between the x-coordinate of Rialto and the x-coordinate of Loma Linda? How long is it?
- Does the vertical line segment represent the difference between the y-coordinate of Rialto and the y-coordinate of Loma Linda? How long is it?
Let's look at the hypotenuse of that triangle:
- What is the Pythagorean Theorem? [Check this Ask Dr. Math FAQ.]
- Use the Pythagorean Theorem to calculate the number of pixels between Rialto and Loma Linda.
If you know how many pixels the distance (as the "crow" flies) between Rialto and Loma Linda, can you convert that to miles?
Converting pixels to miles:
- At the top of the Java applet page, this scale is given:
25 pixels = 1 mile
- Use these ratios to convert pixels to miles:
[Need to understand more about ratios? Check this Ask Dr. Math archive:Figuring Ratios.]
- If you use the number of pixels that you have already calculated in this ratio than you should be able to do some arithmetic to find the distance in miles.
Practice: Find the distances between these other cities in the Inland Empire including:
Fontana and San Bernardino
Muscoy and Loma Linda
Generalize the method that you used to find the distances between the three pairs of cities. Write the steps needed to calculate the distance between any two cities on the map.
Back to Part I