McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
3. Distance and Midpoints
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Exercise 68 Page 34

See solution.

Practice makes perfect

Let's begin by reviewing the Pythagorean Theorem. This theorem tells us that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides and

We want to explain how it is related to the Distance Formula. Then let's draw our triangle it in a coordinate plane.

In the graph we can see the coordinates of the vertices of the triangle. Notice that we can express the lengths of the legs and as a difference in these coordinates. For example, is the difference in the coordinates of points and
Also, is the difference in the coordinates of points and
Let's substitute these values in the equation
Note that we took the positive root of because is the length of a segment, so it is positive. Now, notice that in the graph is the distance between points and The resulting equation is a formula for finding this distance.

Therefore, the Pythagorean Theorem and the Distance Formula are the same equation, only they are written in a different way.