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Analytic Geometry

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Analytic Geometry is a branch of mathematics in which problems are solved using the principles of Geometry and the processes of Algebra.

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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