Introduction to Three Dimensional Geometry | Class 11 Mathematics Notes

11.3 Coordinates of a Point in Space

Once the three-dimensional coordinate system is established, this section explains how to assign coordinates (x, y, z) to a point P in space and conversely how to locate a point given its coordinates. Given a point P, drop a perpendicular PM onto the XY-plane with M as the foot of the perpendicular. From M, draw a perpendicular ML to the x-axis meeting it at L. Let OL = x, LM = y, and MP = z. These three values are the x, y, and z coordinates of point P. The point P(x, y, z) lies in the octant determined by the signs of x, y, and z. Alternatively, through P, draw three planes parallel to the coordinate planes intersecting the x, y, and z axes at points A, B, and C respectively. The coordinates of P are the distances OA = x, OB = y, and OC = z. Conversely, given (x, y, z), locate points A, B, and C on the axes, draw planes through these points parallel to the coordinate planes, and their intersection is the point P. The coordinates represent the perpendicular distances from the YZ, ZX, and XY planes respectively. The origin O has coordinates (0, 0, 0). Points on the x-axis have coordinates (x, 0, 0), and points on the YZ-plane have coordinates (0, y, z). The sign of the coordinates determines the octant in which the point lies, as summarized in Table 11.1.

📊 Diagram: See figure_3: Fig 11.3 shows point P in space with perpendiculars dropped to coordinate planes and axes, defining coordinates x, y, z; Table 11.1 shows sign patterns of coordinates in eight octants.

🔗 Connection: Understanding coordinates leads to the next section where the distance formula between two points in three-dimensional space is derived.

Table on page 3 (4×9)