How Far Between Cities? Part II     
by Suzanne Alejandre

Teacher Lesson Plan

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Open the Java Applet

Note: It will open in a separate window. If you are displaying the page for students, arrange your browser windows so that the applet and the directions can be easily viewed. If students are working individually they should be encouraged to do this.

Ask the question:

How can you find the distance between Rialto and Loma Linda using this map?

Assuming that care has been taken to have horizontal and vertical line segments, prompt students to notice the:

  • display of x (in pixels): How can you calculate how long a line segment is in pixels if you know the x coordinate of both endpoints of that line segment?

  • display of y (in pixels): How can you calculate how long a line segment is in pixels if you know the y coordinate of both endpoints of that line segment?

  • Pythagorean Theorem: Can you find the hypotenuse of a right triangle given the measure of the other two sides of the triangle?

  • scale of pixels to miles: If you know there are 25 pixels in 1 mile, how do you calculate the distance of something in miles given the number of pixels?

NOTE: A pixel is the basic unit of the composition of an image on a computer monitor (usually a single-colored dot).

Students or groups of students working together should complete the following calculations:

Note: The numbers given below are given only as a guideline since there isn't really a place where the students know exactly that they are on the mark for the city location. Students might figure that as long as they're touching the dot somehow, they're on it. Reasonably close answers to what is given below should be accepted.

Rialto is located on the given map: (196, 180)
Loma Linda is located on the given map: (402, 57)
The difference between the two locations on the "x" side of the triangle is 206.
The difference between the two locations on the "y" side of the triangle is 123.
206^2 + 123^2 = 42436 + 15129 = 57565
To find the length of the hypotenuse of the right triangle that was formed, find the square root of 57565. Rounding to the nearest unit, it is about 240.
Using the ratio: 25 pixels/240 pixels = 1 mile/9.6 miles

Rialto is about 9 and a half miles from Loma Linda.

Practice: Ask students to find the distances between other cities in the Inland Empire including:

Fontana and San Bernardino
Muscoy and Loma Linda


Ask students to generalize this method and write an explanation of the steps they would take to calculate the distance between any two cities on the map.

Back to Part I


Math Forum Resources

[Problems of the Week]  [T2T]  [Dr. Math]

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AlgPoW: A Tale of Two Intercepts - posted February 7, 2000
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