The document discusses analytic geometry, which is the merging of algebra and geometry. It defines key concepts like the Cartesian coordinate system, axes, quadrants, and ordered pairs. It then covers the distance formula and how to calculate the distance between two points. Examples are provided to demonstrate finding distances and determining properties of triangles based on point coordinates, such as whether points are collinear or a triangle is equilateral, isosceles, or scalene. Seatwork problems are included for students to practice these concepts.

1. THE STUDY OF ANALYTIC GEOMETRYPrepared by:Mr. Raymond B. Canlapan

2. FLIES

3. ANALYTIC GEOMETRY: DEFINITION AND HISTORYIt is the merging of two branches of Mathematics—algebra and geometry—into a single, unified body of knowledge.ANALYTIC GEOMETRY: DEFINITION AND HISTORYIt is one of the great achievements in mathematics that occurred in the early 1600s.

4. Credit for this great accomplishment goes to the French mathematician Rene Descartes.

5. The same method was also discovered by another famous French mathematician Pierre de Fermat.REVIEW OF CARTESIAN COORDINATE SYSTEMPrepared by:Mr. Raymond B. Canlapan

6. THE CARTESIAN PLANE

7. Define the following:x-axis

8. y-axis

9. Origin

10. Quadrants

11. Ordered pair

12. Abscissa

13. OrdinateREVIEW: PLOT (3, -4)

14. THE DISTANCE FORMULAPrepared by:Mr. Raymond B. Canlapan

15. What is the distance between the two points?

16. Remember:The distance between any two points is computed by the formula 𝑑=𝑥2−𝑥12+𝑦2−𝑦12

17. Example 1:Find the distance between P (0, 1) and Q (3, 5).

18. Example 1:Find the distance between P (2, -2) and Q (6, 1).

19. Example 2:Find the distance between P (-2, -2) and Q (6, 4).

20. Example 3:Find the distance between P (3, 1) and Q (0, -2).

21. Seatwork: Find the distance between the following points:(5, -4) and (5, 4)(10, -1) and (-2, -4)(1, 5) and (7, 5)(-1, -1) and (-2, -2)

22. APPLICATION OF DISTANCE FORMULAPrepared by:Mr. Raymond B. Canlapan

23. PRE-REQUISITE CONCEPTS:Collinear Points -- The points A, B, and C are collinear, with B between A and C, if and only if AB + BC = AC.ABC

24. PRE-REQUISITE CONCEPTS:Triangle – a polygon of three sides. It can be:Equilateral – when all sides are equal