From the video, we conclude that the distance between point A(x1, y1, z1) and B(x2, y2, z2) is
Wednesday, April 29, 2020
Distance Between Two Points
In xy-plane, the distance between P1(x1, y1) and P2(x2, y2) is calculated using Pythagoras theorem,
^2+(y_2-y_1)^2} "|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}")
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In space (three-dimensional system), how do we find the distance between point A and point B? Let's view the video below to find it out. If you want to play around with the points, just click here.
From the video, we conclude that the distance between point A(x1, y1, z1) and B(x2, y2, z2) is
^2+(y_2-y_1)^2+(z_2-z_1)^2} "|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}")
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As such, if P0(x0, y0, z0) is a fixed point and P(x, y, z) is a moving point that moves at a constant distance of a units from P0, we'll get a sphere centered at (x0, y0, z0) with radius a units. The equation of the sphere can be obtained from the concept of distance, i.e.
^2+(y-y_0)^2+(z-z_0)^2=a^2 "(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=a^2")
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You may view the video below to see the forming of the equation using the distance concept.
You may also drag the point P below to see the locus of it. If you want to rotate the 3-D view to have better learning experience, just click here.
Betty, Created with GeoGebra, Screencast-O-Matic and Thomas Calculus, Pearson.
From the video, we conclude that the distance between point A(x1, y1, z1) and B(x2, y2, z2) is
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