July 2010 - Page 3 of 6 - Math and Multimedia

Pythagorean Theorem, Distance Formula, and Equation of a Circle

July 19, 2010 GB High School Geometry, High School Mathematics

In my Algebraic and Geometric Proof of the Pythagorean Theorem post, we have learned that a right triangle with side lengths $a$ and $b$ and hypotenuse length $c$ , the sum of the squares of $a$ and $b$ is equal to the square of $c$ . Placing it in equation form we have $c^2 = a^2 + b^2$ .

If we place the triangle in the coordinate plane, having $A$ and $B$ coordinates of $(x_1,y_1)$ and $(x_2,y_2)$ respectively, it is clear that the length of $AC$ is $|x_2 - x_1|$ and the length of $BC$ is $|x_2 - x_1|$ . We are finding the length, which means that we want a positive value; the absolute value signs guarantee that the result of the operation is always positive. But in the final equation, $c^2 = |x_2 - x_1|^2 + |y_2-y_1|^2$ , the absolute value sign is not needed since we squared all the terms, and squared numbers are always positive. Getting the square root of both sides we have,

$c = \sqrt{|x_2 - x_1|^2 + |y_2-y_1|^2}$

We say that $c$ is the distance between $A$ and $B$ , and we call the formula above, the distance formula. » Read more

11 comments conic sections equation of a circle, derive equation of a circle, distance formula, equation of a circle, equation of a parabola, find equation of a circle, hypotenuse of a right triangle, pythagorean theorem, pythagorean theorem example, pythagorean theorem formula, pythagorean theorem proof, right triangles

GeoGebra Tutorial 25 – The Rolling Circle

July 16, 2010 GB GeoGebra, Software Tutorials

This is the 25^th tutorial in the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

In this tutorial, we use GeoGebra in constructing a rolling circle. This way, we would be able to relate the diameter of the circle to its circumference. Moreover, this activity will reinforce the relationship between the angle and radian measure.

You can view the output of this tutorial here.

Math Teachers at Play #28

July 15, 2010 GB Blog Carnival

The Let’s Play Math Math Teachers at Play #28 Blog Carnival is now available at CTK insights. My article on Introduction to Permutations was one of the accepted entries.

Happy reading!

Leave a comment blog carnival, let's play math

« 1 2 3 4 5 6 »