ANALYTIC GEOMETRY (Lesson 4) Math 14 Plane and Analytic Geometry
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.
DIVISION OF A LINE SEGMENT
Internal Point of Division
External Point of Division
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).
Find the midpoint of the segment joining (7, -2) and (-3, 5).
The line segment from (1, 4) to (2, 1) is extended a distance equal to twice its length. Find the terminal point.
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.
Find the trisection points of the line joining (-6, 2) and (3, 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.
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