Tiêu đề LECTURE NOTES DAY 08_ANALYTIC GEOMETRY 1.pdf ✅

MATHEMATICS, SURVEYING, TRANSPORTATION ENGINEERING, AND CONSTRUCTION presented by: Engr. King Justine H. Guardario Kippap Civil Engineering ANALYTIC GEOMETRY
DAY 8: ANALYTIC GEOMETRY A logo with a white letter Description automatically generated LECTURE OUTLINE • Coordinate System • 2-Dimensional Coordinate System • Cartesian • Polar • 3-Dimensional Coordinate System • Cartesian • Cylindrical • Spherical • Transformation of Coordinate Systems • Equations in Other Coordinate Systems • Polar Coordinates • Parametric Equations • Lines and Distances • Line Properties • Slope Formula • Division of a Line Segment • Midpoint • Internal and External Division Points • Parallel Lines • Perpendicular Lines • Angle Between Lines • Equation of a Line • Two-point Form • Point-slope Form • Slope-intercept Form • Intercept Form • Standard and General Form • Normal Form • Distances • Distance between two points • Distance from a point to a line • Distance between parallel lines • Area of a polygon with given coordinates • Locus of a Point • Line • On Conic Sections From finding slopes to finding success—keep solving, Engineer!
DAY 8: ANALYTIC GEOMETRY COORDINATE SYSTEM From finding slopes to finding success—keep solving, Engineer! Coordinates are helpful in numerically describing the position of elements on a manifold. 1. 2-Dimensional Coordinate System 1.1 Cartesian Coordinate System A logo with a white letter Description automatically generated x – coordinate = abscissa y – coordinate = ordinate 0 , 0 = origin x-axis y-axis . 1 x (x, y) y (0,0) + x-axis + y-axis - y-axis - x-axis Quadrant I (+ , +) Quadrant II (− , +) Quadrant III (− , −) Quadrant IV (+ , −)
DAY 8: ANALYTIC GEOMETRY COORDINATE SYSTEM From finding slopes to finding success—keep solving, Engineer! Coordinates are helpful in numerically describing the position of elements on a manifold. 1. 2-Dimensional Coordinate System 1.2 Polar Coordinate System It is a coordinate system that describes the position of a point by using its direct distance from the origin and its azimuth. A logo with a white letter Description automatically generated . r 1 θ (r, θ) r = radius Note: Pole is the reference point Polar Axis is the line segment ray from the pole in the reference direction