![]() ![]() ![]() To take us from his theorem of the relationships among sides of right triangles to coordinate grids, the mathematical world had to wait for René Descartes. Pythagoras was a generous and brilliant mathematician, no doubt, but he did not make the great leap to applying the Pythagorean theorem to coordinate grids. You are also able to relate the Distance Formula to the Pythagorean Theorem. Now that you have worked through the lesson and practice, you are able to apply the Distance Formula to the endpoints of any diagonal line segment appearing in a coordinate, or Cartesian, grid. You need not construct the other two sides to apply the Distance Formula, but you can see those two "sides" in the differences (distances) between x-values (a horizontal line) and y- values (a vertical line). The distance formula gets its precision and perfection from the concept of using the angled line segment as if it were the hypotenuse of a right triangle formed on the grid. You really should be able to take the last few steps by yourself. Here are the beginning steps, to help you get started:ĭ = ( 10 − ( − 2 ) ) 2 + ( 1 − 4 ) 2 D=\sqrt D = ( − 10 ) 2 + ( − 4 ) 2 We will not leave you hanging out on a diagonal. ![]()
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