TABLE OF CONTENTS Let P be any point in space. Through P, draw planes parallel to the three coordinate planes meeting the coordinate axes in the points A, B and C respectively. Then if OA = x, OB = y and OC = z the three numbers x, y, z taken in this order are called the Cartesian coordinates of the point P and we refer the point P as P( x, y, z). Any of the numbers x, y, z will be positive or negative depending on whether it is measured from O along the corresponding axis in the positive or negative direction.
Some other ways of defining the coordinates of a point
We have seen that in order to determine the coordinates of a point P, we have to draw three planes through P respectively parallel to YZ, ZX and XY-planes. The three planes through P and the three coordinate planes form a rectangular parallelopiped which has six rectangular faces consisting of three pairs of parallel planes, viz. PMAN, LCOB ; PNBL, MAOC ; PLCM, NBOA.
x = OA = CM = LP = perpendicular distance of P from YZ-plane
y = OB = AN = MP = perpendicular distance of P from ZX-plane
z = OC = AM = NP = perpendicular distance of P from XY-plane
Thus, the coordinates x, y, z of a point P are the perpendicular distances of P from...
