1. CO-ORDINATE
GEOMETRY
A.VICTORIYA WINSE ANGELIN
21EDM05

2. INDEX
 INTRODUCTION
 MAPPING THE PLANE
 DISTANCE BETWEEN TWO POINTS
 PROPERTIES OF DISTANCE
 MIDPOINT OF A LINE SEGMENT

3. INTRODUCTION
The French Mathematician Rene Descartes developed
a new branch of Mathematics known as Analytical
Geometry or Coordinate Geometry.
Coordinate geometry (or analytic geometry) is defined
as the study of geometry using the coordinate points.
Using coordinate geometry, it is possible to find the
distance between two points, dividing lines in m:n
ratio, finding the mid-point of a line, calculating the
area of a triangle in the Cartesian plane, etc.

4. MAPPING THE PLANE
Draw a perpendicular line and mark X-axis and Y-axis.
In horizontal line the positive numbers lie on right side of
zero and negative numbers on left side of the zero.
In vertical line the positive numbers lie above zero and the
negative numbers lie below zero.
The x co-ordinate is called the Abscissa and the y co-
ordinate is called the Ordinate.
The X and Y axis divides the plane into four regions , they
are called as Quadrants.

6. Plot ( -4 , -2 )
To plot the points (-4,-2) in the Cartesian coordinate plane. We
follow the x-axis until we reach -4 and draw a vertical line at x = -4
Similarly follow the y-axis until we reach -2 and draw a horizontal
line at y = -2

7. DISTANCE BETWEEN THE TWO POINTS
Distance between two points is the length
of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is
usually given by d=√((x2 – x1)² + (y2 – y1)²).

8. PROPERTIES OF DISTANCE
 COLLINEAR
Dis (A,B) + Dis (B,C) = Dis (A,C)
 EQUILATERAL TRIANGLE
Dis (A,B) = Dis (B,C) = Dis (C,A)
 ISOSCELES TRIANGLE
Dis (A,B) = Dis (B,C) or
Dis (A,B) = Dis (C,A)

9.  PARALLELOGRAM
Dis (A,B) = Dis (C,D)
Dis (A,D) = Dis (B,C)
 RHOMBUS
Dis (A,B) = Dis (B,C) = Dis (C,D) = Dis (D,A)

10. MIDPOINT OF A LINE
SEGMENT
The midpoint of a segment is the point on the segment
that is equidistant from the endpoints.
In the above diagram,
B is the midpoint of A and C.