ANALYTIC GEOMETRYMath 004

Lecture #1• Rectangular Coordinate System• Distance Between Two Points• Division of a Line Segments• Midpoint of a Line

RECTANGULAR COORDINATE SYSTEM

Developed by Rene Descartes

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

Ex. Plot the ff. points in Cartesian plane

DISTANCE BETWEEN TWO POINTS

The distance between two points of the plane with Cartesian coordinates   and   is

Sample Problem

1. Calculate the distance of AB

2. Calculate the distance of AB

3. Find the value of if the distance between two points is units.

4. Is the triangle with the vertices isosceles?

5. Determine the lengths of the diagonals of the trapezoid with vertices A(–3, 3), B(12, 8), C(7, 6),D(0, 7)

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

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

MIDPOINT OF A LINEThe point halfway between the endpoints of a

line segment is called the midpoint. A midpoint divides a line segment into two equal segments.

The midpoint of a segment with endpoints and has coordinates of