When we study the motion of body then its displacement is described on cartesian plane or in 3d geometry and not in real physical conditions,in this way to calculate the distance travelled by the body is a major aspect in calculating its speed and other things,and here distance formula help us to do so.There are many other importance of distance formula...
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If you know the end points then use the distance formula or simply use a ruler.
it is not important
if no geometry in our life, we can't do the other things if we dont have geometry.
Distance = Rate x Time * * * * * Or it could be the area under the speed-time graph. Or, in coordinate geometry, the distance between the points with coordinates (w,x) and (y,z) which is sqrt[(w - y)2 + (x - z)2]. There are analogous formulae for three or more dimensions.
In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.