Review of Analytic Geometry

Plane Geometry: To locate the position of point P in a two-dimensional space, we can use either the rectangular coordinates (x,y) or the polar coordinates (r, θ). The transformation between these two coordinate systems takes the form

(1) or (2)

To calculate the distance d between points P1 and P2, we use

(3) The slope of the line connecting points P1 and P2 is given by (4) To describe the straight line that passes through points P1 and P2, we use (5) where m is the slope of the line and b is the y intercept, which is found by knowing m and the coordinates of any point on the line. For example, if we were to use the coordinates of point P1, then we have

Solid Geometry: To locate the position of point P in a three-dimensional space, we can use either the rectangular coordinates (x,y,z) or the cylindrical coordinates (r,θ,z). The transformation between these two coordinate systems takes the form

(6) or (7)

where θ is measured from the x axis.