The document discusses key concepts in analytic geometry covered in Lecture #1: 1) It introduces the rectangular coordinate system developed by Descartes with perpendicular x and y axes intersecting at the origin, dividing the plane into four quadrants. 2) It discusses calculating the distance between two points in the plane and dividing a line segment internally or externally. 3) It defines the midpoint of a line as the point that splits the line segment into two equal parts.

1. ANALYTIC GEOMETRY
Math 004
Lecture #1
• Rectangular Coordinate System
• Distance Between Two Points
• Division of a Line Segments
• Midpoint of a Line

2. RECTANGULAR COORDINATE
SYSTEM
 Developed by Rene Descartes

3.  The horizontal axis is the x-axis and the vertical
axis is the y-axis
 The point of intersection of the two axes is the
origin of the Cartesian plane
 The Cartesian plane is composed of four
quadrants
 Each quadrant represents an ordered pair with
respective sign
 Plotting is the process of locating point/s in the
Cartesian plane

4. Ex. Plot the ff. points in Cartesian plane

5. DISTANCE BETWEEN TWO
POINTS


6. Sample Problem
1. Calculate the distance of AB

7. 2. Calculate the distance of AB

8. 

9. DIVISION OF A LINE SEGMENT
 When P lies between A and B on the line
segment, then P is said to be divided
internally (internal division)
A P B

10.  When points, such as Q and R, lie on an
extension of the segment outside the interval
AB, then they are said to be divided externally
(external division)
Q A B R

11. MIDPOINT OF A LINE
