3. Distance and Midpoints
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Represent the Pythagorean Theorem in a coordinate plane.
See solution.
Let's begin by reviewing the Pythagorean Theorem. This theorem tells us that the square of the length of the hypotenuse c of a right triangle equals the sum of the squares of the lengths of the other two sides a and b.
We want to explain how it is related to the Distance Formula. Then let's draw our triangle it in a coordinate plane.
a=y2−y1, b=x2−x1
LHS=RHS
a2=a
Therefore, the Pythagorean Theorem and the Distance Formula are the same equation, only they are written in a different way.