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He is regarded as the founder of Analytic geometry by introducing coordinates system in 1637.

René Descartes

The Cartesian Coordinate System

* also known as Rectangular Coordinate System or xy-Coordinate System. * It is made up of two mutually perpendicular number lines with the same unit of length and intersecting at their origin. The origin of its number line is its zero point. * The number lines are called the coordinate axes. * The horizontal line is called the x-axis and the vertical line is called the y-axis. * The coordinate axes divide the whole plane into four regions called quadrants. * The plane on which these axis are constructed is called the Coordinate Plane or xy-plane. * The distance of any point P from the y-axis is called x-coordinate or abscissa of the point P. * The distance of any point P from the x-axis is called the y-coordinate or ordinate of the point P. * The pair of real numbers (x,y) is called the coordinate pair of point P. * The symbol P(x,y) is used to indicate the point P on the plane with abscissa x and ordinate y. * The signs of the coordinates determine the quadrant where the point lies. * QI: (+,+) QIII: (-,-)

QII: (-,+) QIV: (+,-)

Exercise 1.1

Indicate the quadrant or the axis on which the point lies. 1. A(3,-2) 6. F(5,0) 2. B(-1,5) 7. G(4,-1) 3. C(2,1) 8. H(0,2) 4. D(0,-4) 9. I(-3,-3) 5. E(-1,-2) 10. J(0,0)

Determine the coordinates of the points in the Cartesian plane.

11. P1

12. P2

13. P3

14. P4

15. P5

Plot the given points in the coordinate…...

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