It is sqrt(3)/2 = 0.8660 approx.
Displacement is a value predicated on the shortest distance between an initial and final position. If a "body" moves a certain distance and returns to its original origin it has not technically traveled any distance based on this definition. The displacement will therefore be zero
19.92486 (rounded)
17
Distance from (0, 0) to (5, 12) using distance formula is 13
Absolute Value
1
7.62
The displacement of an object that moves from the origin to a position at -12m is -12m. Displacement is a vector quantity that represents the shortest distance and direction from the initial to the final position of an object. In this case, the negative sign indicates that the final position is in the opposite direction from the origin.
There is a slight difference in color, but a great distance between their countries of origin.
3
To find the distance between the origin and the point (x,y) use Pythagoras on the right angled triangle which has the points (0, 0), (x, 0), (x, y) - the distance is the hypotenuse of the triangle and so has length: distance = √(x2 + y2) This can be extended to find the distance between any two points (x1, y1) and (x2, y2): distance = √((x2 - x1)2 + (y2 - y1)2) (for the original question (x1, y1) is the origin (0, 0) and the first formula results.)
According to http://mathworld.wolfram.com/RadiusVector.html the radius vector (often written as r hat, or the letter r with a carrot ^ over it) is just the distance from the origin to the point of interest. So the magnitude is the distance between the point and the origin, and the direction is the direction from the origin to the point.