Introduction to Three Dimensional Geometry

In three dimensions, the coordinate axes of a rectangular Cartesian coordinate system are three mutually perpendicular lines. The axes are called the x, y and z axes. The three planes determined by the pair of axes are the coordinate planes. These planes are called xy, yz and zx planes and they divide the space into eight regions known as octants. The coordinates of a point P in the space are the perpendicular distances from P on three mutually perpendicular coordinate planes YZ, ZX and XY respectively. The coordinates of a point P are written in the form of a triplet (x,y,z). The coordinates of any point on: • x-axis are of the form (x, 0, 0) • y-axis are of the form (0, y, 0) • z-axis are of the form (0, 0, z) • XY-plane are of the form (x, y, 0) • YZ-plane are of the form (0, y, z) • XZ-plane are of the form (x, 0, z) The point of intersection of the medians of a triangle is centroid. The position of each point on the plane is determined with reference to the rectangular axes by means of a pair of numbers called coordinates which are the perpendicular distances of the point from the axes. Three or more points that lie on the same straight line are said to be collinear. The Cartesian plane, named after the mathematician Rene Descartes (1596 - 1650), is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers. A closed figure made up of line segments is called polygon. A three dimensional figure in which all faces are rectangular and all the angles formed by any two intersecting planes are right angles, is called rectangular parallelepiped. Keywords: Coordinates of centroid of a triangle, coordinates of the mid-point of the line segment joining two points

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