![]() They belong to a straight line that it's neither horizontal nor vertical. In fact, let's think about computing the distance between the points #A# and #C# previously defined. This is quite easy, because the two points lie on the horizontal line #y=3#, so the distance between them can be interpreted as the length of the line segment #AB#, which is #5# and can be computed by subtracting the #x#-coordinates of the two points and considering the absolute value of the result (to avoid negative distances). a plane with a coordinate system such that).įirst of all, let's compute the distance between #A=(2,3)# and #B=(7,3)#. It's used to compute the distance between two points in an orthogonal coordinate system (i.e. The distance formula makes sense in a coordinate context. In other words, they are the same thing in two seemingly different contexts. In short, the distance formula is a formalization of the Pythagorean Theorem using #x# and #y# coordinates. (depending on if #x_1 > x_2# or #x_1 < x_2#, and similarly for #y#.) Or, we could put it another way through substitutions based on the distance definitions above. What do you see in these formulas? Have you ever tried drawing a triangle on a Cartesian coordinate system? If so, you should see that these are two formulas relating the diagonal distance on a right triangle that is composed of two component distances #x# and #y#. The greater the #x# contribution, the flatter the slope. The greater the #y# contribution, the steeper the slope.
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