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# Math14 lesson 3

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### Math14 lesson 3

1. 1. ANALYTIC GEOMETRY (Lesson 4) Math 14 Plane and Analytic Geometry
2. 2. OBJECTIVES : At the end of the lesson, the student is expected to be able to: • Determine the coordinates of a point of division of a line segment. • Define the median of the triangle.
3. 3. DIVISION OF A LINE SEGMENT
4. 4. Internal Point of Division
5. 5. External Point of Division
6. 7. <ul><li>Examples : </li></ul><ul><li>The line segment joining (-5, -3) and (3, 4) is to be divided into five equal parts. Find the point of division closest to (-5, -3). </li></ul><ul><li>Find the midpoint of the segment joining (7, -2) and (-3, 5). </li></ul><ul><li>The line segment from (1, 4) to (2, 1) is extended a distance equal to twice its length. Find the terminal point. </li></ul><ul><li>On the line joining (4, -5) to (-4, -2), find the point which is three-seventh the distance from the first to the second point. </li></ul><ul><li>Find the trisection points of the line joining (-6, 2) and (3, 8). </li></ul><ul><li> </li></ul>
7. 8. 6. The line segment joining a vertex of a triangle and the midpoint of the opposite side is called the median of the triangle. Given a triangle whose vertices are A(4,-4), B(10, 4) and C(2, 6), find the point on each median that is two-thirds of the distance from the vertex to the midpoint of the opposite side.
8. 9. REFERENCES Analytic Geometry, 6 th Edition, by Douglas F. Riddle Analytic Geometry, 7 th Edition, by Gordon Fuller/Dalton Tarwater Analytic Geometry, by Quirino and Mijares