13.13.4  The coordinates of a point, vector or line in the plane: coordinates

See Section 14.12.4 for coordinates in three-dimensional geometry.

The coordinates finds the coordinates of a point or two points that determine a line.

• coordinates takes one argument:
  X, either a point, a sequence or list of points, or a line.
• coordinates(X) returns:
  • a list consisting of the abscissa and ordinate of X, if X is a point or a vector, or a sequence or list of such lists, if X is a sequence or list of points.
  • a list of two points on the line X, in the order determined by the direction of the line, if X is a line.

Examples.

• Input:
  coordinates(1+2*i)
  or:
  coordinates(point(1+2*i))
  or:
  coordinates(vector(1+2*i))
  Output:

  ⎡ ⎣

  1,2

  ⎤ ⎦

• Input:
  coordinates(point(1+2*i) - point(i))
  or:
  coordinates(vector(i,1+2*i))
  or:
  coordinates(vector(point(i),point(1+2*i)))
  or:
  coordinates(vector([0,1],[1,2]))
  Output:

  ⎡ ⎣

  1,1

  ⎤ ⎦

• Input:
  d:= line(-1+i,1+2*i)
  or:
  d:= line(point(-1,1),point(1,2))
  then:
  coordinates(d)
  Output:

  ⎡ ⎣

  −1+i,1+2 i

  ⎤ ⎦

• Input:
  coordinates(line(y = (1/2 * x + 3/2)))
  Output:

  ⎡ ⎢ ⎢ ⎣

  3 i 2

  ,1+2 i

  ⎤ ⎥ ⎥ ⎦

• Input:
  coordinates(line(x - 2*y + 3 = 0))
  Output:

  ⎡ ⎢ ⎢ ⎣

  3 i 2

  ,

  −4+i 2

  ⎤ ⎥ ⎥ ⎦

• Input:
  coordinates(i,1+2*i)
  or:
  coordinates(point(i),point(1+2*i))
  Output:

  ⎡ ⎣

  0,1

  ⎤ ⎦

  ,

  ⎡ ⎣

  1,2

  ⎤ ⎦

• Note that if the argument is a list of real numbers, it is interpreted as a list of points on the real axis.
  Input:
  coordinates([1,2])
  Output:

  ⎡ ⎢ ⎣

  1 0 2 0

  ⎤ ⎥ ⎦