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# Analytic geom and distance formula

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### Analytic geom and distance formula

1. 1. THE STUDY OF ANALYTIC GEOMETRY<br />Prepared by:<br />Mr. Raymond B. Canlapan<br />
2. 2. FLIES<br />
3. 3. ANALYTIC GEOMETRY: DEFINITION AND HISTORY<br /><ul><li>It is the merging of two branches of Mathematics—algebra and geometry—into a single, unified body of knowledge.</li></li></ul><li>ANALYTIC GEOMETRY: DEFINITION AND HISTORY<br /><ul><li>It is one of the great achievements in mathematics that occurred in the early 1600s.
4. 4. Credit for this great accomplishment goes to the French mathematician Rene Descartes.
5. 5. The same method was also discovered by another famous French mathematician Pierre de Fermat.</li></li></ul><li>REVIEW OF CARTESIAN COORDINATE SYSTEM<br />Prepared by:<br />Mr. Raymond B. Canlapan<br />
6. 6. THE CARTESIAN PLANE<br />
7. 7. Define the following:<br /><ul><li>x-axis
8. 8. y-axis
9. 9. Origin
11. 11. Ordered pair
12. 12. Abscissa
13. 13. Ordinate</li></li></ul><li>REVIEW: PLOT (3, -4)<br />
14. 14. THE DISTANCE FORMULA<br />Prepared by:<br />Mr. Raymond B. Canlapan<br />
15. 15. What is the distance between the two points?<br />
16. 16. Remember:<br />The distance between any two points is computed by the formula <br />𝑑=𝑥2−𝑥12+𝑦2−𝑦12<br /> <br />
17. 17. Example 1:<br />Find the distance between P (0, 1) and Q (3, 5).<br />
18. 18. Example 1:<br />Find the distance between P (2, -2) and Q (6, 1).<br />
19. 19. Example 2:<br />Find the distance between P (-2, -2) and Q (6, 4).<br />
20. 20. Example 3:<br />Find the distance between P (3, 1) and Q (0, -2).<br />
21. 21. Seatwork: Find the distance between the following points:<br />(5, -4) and (5, 4)<br />(10, -1) and (-2, -4)<br />(1, 5) and (7, 5)<br />(-1, -1) and (-2, -2)<br />
22. 22. APPLICATION OF DISTANCE FORMULA<br />Prepared by:<br />Mr. Raymond B. Canlapan<br />
23. 23. PRE-REQUISITE CONCEPTS:<br /><ul><li>Collinear Points -- The points A, B, and C are collinear, with B between A and C, if and only if </li></ul>AB + BC = AC.<br />A<br />B<br />C<br />
24. 24. PRE-REQUISITE CONCEPTS:<br />Triangle – a polygon of three sides. It can be:<br /><ul><li>Equilateral – when all sides are equal
25. 25. Isosceles – when two sides (legs) are equal
26. 26. Scalene – when no sides equal</li></li></ul><li>EXAMPLE # 1:<br />Points D (1, 3), E (-1, -1), and F (-3, -2) are in a plane. Are these collinear?<br />
27. 27. EXAMPLE # 2:<br />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?<br />
28. 28. EXAMPLE # 3:<br />The vertices of a triangle are at E (4, 0), F (2, 1), and G (-1, -5). What kind of triangle is it?<br />
29. 29.
30. 30. Seatwork:<br />Plot the points (0, 0), (-3, -3) and (4, 4) and state whether they are collinear or not.<br />Show that the points A (2, 6), B (-3, -3) and C (6, 2) are vertices of an isosceles triangle. <br />