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Division of a Line Segment Into Equal Parts
1.
DIVISION OF A
LINE SEGMENT Prepared by: Prof. Teresita P. Liwanag ā Zapanta B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)
2.
DIVISION OF A
LINE SEGMENTĀ POINT OF DIVISION āĀ isĀ aĀ pointĀ thatĀ dividesĀ aĀ lineĀ segmentĀ toĀ aĀ givenĀ ratio.
3.
ByĀ SimilarĀ Triangles:
xĀ āĀ x1Ā =Ā rx2Ā āĀ rx rxĀ +Ā xĀ =Ā x1Ā +Ā rx2 x(Ā 1Ā +Ā rĀ )Ā =Ā x1Ā +Ā rx2 SolvingĀ forĀ x Ā Ā Ā Ā Ā Ā Ā solvingĀ forĀ y
4.
Examples: 2.TheĀ lineĀ segmentĀ
joiningĀ (-5,Ā -3)Ā andĀ (3,Ā 4)Ā isĀ toĀ beĀ dividedĀ intoĀ fiveĀ equalĀ parts.Ā FindĀ theĀ pointĀ ofĀ divisionĀ closestĀ toĀ Ā Ā Ā Ā Ā (-5,Ā -3). 3.FindĀ theĀ midpointĀ ofĀ theĀ segmentĀ joiningĀ (7,Ā -2)Ā andĀ Ā (-3,Ā 5). 4.TheĀ lineĀ segmentĀ fromĀ (1,Ā 4)Ā toĀ (2,Ā 1)Ā isĀ extendedĀ aĀ distanceĀ equalĀ toĀ twiceĀ itsĀ length.Ā FindĀ terminalĀ point. 5.OnĀ theĀ lineĀ joiningĀ (4,Ā -5)Ā toĀ (-4,Ā -2),Ā findĀ theĀ pointĀ whichĀ isĀ three-seventhĀ theĀ distanceĀ fromĀ theĀ firstĀ toĀ theĀ secondĀ point.Ā 6.FindĀ theĀ trisectionĀ pointsĀ ofĀ theĀ lineĀ joiningĀ (-6,Ā 2)Ā andĀ (3,Ā 8).Ā 7.TheĀ midpointsĀ ofĀ theĀ sidesĀ Ā ofĀ aĀ triangleĀ areĀ A(3,Ā 0),Ā B(5,Ā 2),Ā C(2,Ā 2). 8.ThreeĀ consecutiveĀ verticesĀ ofĀ aĀ parallelogramĀ areĀ A(6,Ā 1),Ā Ā B(-2,Ā 3),Ā C(-6,Ā 0).Ā FindĀ theĀ coordinatesĀ ofĀ theĀ fourthĀ vertex. Ā Ā Ā Ā Ā Ā Ā Ā
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