COORDINATE GEOMETRY

A full description and study material of coordinate geometry for class 9

1. STANDARD NINE TERM-II MATHEMATICS CO-ORDINATE GEOMETRY By, DARSHINI.A.

2. CONTENTS What is co-ordinate geometry? Devising a co-ordinate system Distance between any two points Properties of distance The midpoint of a line segment Points of trisection of a line segment Section Formula The coordinates of the centroid

3. What is co-ordinate geometry?

4. A system of geometry where the position of points on the plane is described using an ordered pair of numbers.

5. FOUNDER OF CO-ORDINATE GEOMETRY

6. The French Mathematician Rene Descartes (1596-1650) developed a new branch of mathematics called the Analytical Geometry or Co-ordinate Geometry which combined all arithmetic, algebraic and geometry of the past ages in a single technique of visualising as points on a graph and equations as geometrical shapes.

7. DEVISING A CO-ORDINATE SYSTEM: Co-ordinate plane: It has two scales – one running across the plane called the “x-axis” and another a right angle to it called the “y-axis” . The point where the axes cross is called the “ Origin ” and is where both x and y are zero.

8. The x co-ordinate Is called the Abscissa and the y co-ordinate is called the Ordinate. The x-axis and the y-axis divide the plane into four regions called the Quadrants.They are usually numbered as I, II, III and IV.

9. The “straight line distance” is usually called as “the crow flies”. Distance between two points on the co-ordinate axes Distance between two points lying on a line parallel to coordinate axes Distance between two Points on a plane DISTANCE BETWEEN ANY TWO POINTS:

10. Distance between two points on the co-ordinate axes: Points on x-axis: If two points lie on the x-axis , then the distance between them is equal to the difference between the x co-ordinates. Points on y-axis: If two points lie on the y-axis, then the distance between them is equal to the difference between the y co-ordinates.

11. Distance between two points on a plane:

12. Properties of distance: The sum of the distance between two pairs of points is equal to the third pair of points. In other words, points A, B, C are collinear if AB+BC=AC. The sum of the squares of two sides is equal to the square of the third side , which is the hypotenuse of a right angled triangle. The opposite sides of a parallelogram are equal.

13. THE MIDPOINT OF A LINE SEGMENT:

14. POINTS OF TRISECTION OF A LINE SEGMENT:

15. SECTION FORMULA:

16. THE COORDINATES OF THE CENTROID: