From Geometry to Coordinate Geometry
Geometry appears to have originated from the need for measuring land. Today, geometry is a branch of mathematics in which we study the properties of various figures
Covers the historical roots of geometry, the axiomatic approach of Euclid, the analytic approach of Descartes, and the rectangular Cartesian coordinate system with its quadrants.
Covers directed distance (signed length) between points on horizontal and vertical segments, and the distance formula derived from the Pythagorean theorem.
Covers the midpoint formula and the general section formula for a point dividing a segment internally in a given ratio.
Covers the definition of the angle of inclination, the slope of a nonvertical line, and the relation tan(theta) = slope.
Covers the concept of a locus, the three-step method for finding the equation of a locus, and several worked loci based on distance conditions.
Covers the equations of horizontal and vertical lines, and the point-slope, slope-intercept, two-point, and intercept forms of the equation of a nonvertical line.
Covers the general form Ax+By+C=0, its slope and intercepts, the slope conditions for parallel and perpendicular lines, and the formula for the angle between two lines.
Covers the pole, polar axis, directed angle, negative values of r, multiple representations of the same point, and the relations between polar and Cartesian coordinates.