Cartesian plane
This document provides information about various landmarks and their locations: Rizal Park in Manila, New York City in the USA, the Eiffel Tower in Paris, the Merlion in Singapore, and the Basilica of Saint Peter in Rome. It then instructs the reader to locate each of these places on a map according to their latitude and longitude. The document explains how Cartesian coordinates use a grid system with x and y axes to precisely locate points on a plane or map. It provides examples of plotting points in the Cartesian plane's four quadrants and identifying points' coordinates. The document distinguishes between points that lie within the quadrants versus along the axes. It concludes with an activity asking the reader to identify quadrant locations for
Cartesian plane
- 5. New York City, USA
- 11. The Basilica of Saint Peter - Rome
- 12. LOCATE EACH OF THESE PLACES ON THE MAP
- 14. NOTE: A place on the map is described according to latitude and longitude. Illustrate how a place on the map can be located using the latitude and longitude, and vice versa.
- 16. René Descartes, 1596 - 1650
- 17. René Descartes • Cartesian mathematics was invented by (and is named after) French philosopher, physiologist, and mathematician René Descartes, 1596 - 1650. • Descartes is famous not just for inventing Cartesian mathematics, which at the time was a stunning unification of algebra and geometry. He is also well-known for making a pretty good stab of answering the question “How do I know something is true?”, a question that has kept generations of philosophers happily employed.
- 18. Points and their Coordinates y axis x axis origin y axis – the vertical line or the axis of the ordinates. x axis – horizontal line or the axis of the abscissa. Origin – the intersection of the axes.
- 19. The Cartesian Plane is divided into four quadrants. III III IV (+,+) (-,+) (-,-) (+,-)
- 20. Plotting Points in the Cartesian Plane 5 4 (5, 4) is an example of an ordered pair x coordinate y coordinate ( 5 , 4 )
- 21. Plotting Points in the Cartesian Plane (5, 4) is an example of an ordered pair ( 5 , 4 ) Quadrant I
- 22. Example 1: It is like entering a hotel. Plot (-3,4) (x in the door Up the elevator (– 3, left 3 up 4 , y) 4)
- 23. Plot ( -3, 4) (-3 , 4) Quadrant II
- 24. Example 2. Identify the coordinates of points C, D, E and F. In which quadrant is each point located?
- 25. Example 2. Identify the coordinates of points C, D, E and F. In which quadrant is each point located? (x, y) - Quadrant C (4,5) - QI D (3,-5) - QIV E (-5,2) - QII F (-3,-3) - QIII
- 26. Try This! Identify the coordinates of points L, N and O. In which quadrant is each point located?
- 27. Example 3.Plot the following points. E(5, 0) F(0, 6) G(– 4, 0) H(0, – 3)
- 28. F(0, 6) G(– 4, 0) H(0, – 3) E(5, 0)
- 29. What do you notice about their coordinates?
- 30. All points lie on the axes, not in quadrants
- 31. The Cartesian Plane is divided into four axes. Along positive y axis Along positive x axis Along negative y axis Along negative x axis
- 32. Activity In what quadrant or axis is each point located 1.(-2 , -2) 2.(4, -6) 3.(0 , 5) 4.( 5, 8) 5.( -4, 5) 6. ( 4, 0) 7. (.5 , 0) 8. (3 , 4) 9. ( 4, 7) 10. (- 2.5, 6)
- 33. Part II. Write a generalization 1. In which quadrant do points lie if both their abscissa and ordinate is positive? 2. In which quadrant do points lie if their abscissa is zero? 3. In which quadrant do points lie if both their ordinate is a negative real number? 4. In which quadrant do points lie if both their abscissa and ordinate is negative? 5. n which quadrant do points lie if their ordinate is zero?
- 34. THANK YOU