Discovering the Distance Formula

Given two points with coordinates (x1,y1) and (x2,y2), what is the distance between the two points? Let's try to discover this formula. Look at the triangles below. You can count spaces to figure out the "rise" and the "run". These two numbers are the legs a and b of your right triangle. You want to find out how long the hypotenuse c is. So, use a^2 + b^2 = c^2 to figure these lengths out!

Now that you have worked with some numbers, let's generalize this procedure to get the DISTANCE FORMULA. The following hints will help you to find it and PROVE it at the same time. If you get stuck, click the HAND button and it will show the answers to each step.

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