Distance formula geometry1/23/2024 ![]() ![]() The distance formula is commonly seen as: D sqrt((x1 - x2)2 + (y1 - y2)2) We commonly write the Pythagorean Theorem as: c sqrt(a2 + b2) Consider the following major points (in Euclidean geometry on a Cartesian coordinate axis): The definition of a distance. Learn the derivation of the distance formula and use it to measure the distance between points. ![]() If you end up with a negative value under the square root in the very end, it's a sign you did something wrong! Make sure to use parentheses if you're plugging this into a calculator.ĭouble check with your teacher to see if you should be giving your answer in simplified radical form ( How do you simplify a radical?) or as a rounded decimal ( How do you round a decimal?). If we consider what the distance formula really tells you, we can see the similarities. Understand the distance formula and its definition as per geometry. It doesn't matter in the end because you square the value so it will come out positive either way. ![]() The length of the leg is actually the absolute value of the difference. It just depends on the order that you labeled the points, sometimes you're going to get a negative value when you subtract. If you look at the graph, you can see that the length of the vertical leg is a positive 6. When you subtract the y-coordinates you get -6. This will help you visualize how far apart they really are. Keep in mind that if the coordinates have different signs, it means they're on the opposite sides of the axis. Make sure to remember that subtracting is the same thing as adding the opposite. ![]()
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