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

2. FLIES

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

6. THE CARTESIAN PLANE

8. y-axis

9. Origin

10. Quadrants

11. Ordered pair

12. Abscissa

14. THE DISTANCE FORMULA Prepared 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 FORMULA Prepared by: Mr. Raymond B. Canlapan

25. Isosceles – when two sides (legs) are equal

27. EXAMPLE # 2: The following are the coordinates of the three points which are the vertices of a triangle: (8, -3), (-3, 4), and (6, 6). Is the triangle equilateral, isosceles or scalene?

28. EXAMPLE # 3: The vertices of a triangle are at E (4, 0), F (2, 1), and G (-1, -5). What kind of triangle is it?

30. Seatwork: Plot the points (0, 0), (-3, -3) and (4, 4) and state whether they are collinear or not. Show that the points A (2, 6), B (-3, -3) and C (6, 2) are vertices of an isosceles triangle.