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Finding the Distance between two Points



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In this section, we learn how to find the distance between two points on a coordinate plane. We begin by learning about the Pythagorean formula: a2 + b2 = c2. This formula is a relationship between the sides of a right triangle. Using our Cartesian coordinate plane, we can connect any two points (x1,y1),(x2,y2) using a line. This line represents the hypotenuse of the right triangle. After this is completed, we can draw lines to represent legs a and b. These legs are the horizontal and vertical legs of the right triangle. We can measure the lengths of leg a, along with leg b, and plug the results into the Pythagorean formula. This will allow us to solve for c (the hypotenuse) or distance between our two points. The distance formula is a direct application of this process. Instead of having to pull out a coordinate plane each time, we can simply label each point and plug into the formula. It relates c (the distance between the two points) to the square root of a2 + b2. a and b here represent the horizontal leg and vertical leg in the right triangle.
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