Q. 33.6( 8 Votes )

Prove that the origin O divides the line segment joining the points, A(1, –3) and B(–3, 9) in the ratio 1 : 3 internally. Find the coordinates of the points dividing externally.

Answer :

Internal divison formula:


Coordinates of a point P(x,y) dividing the line segment joining A (x1, y1) and B (x2, y2) in the ratio m:n internally are


Let O divide the line segment joining the given points in the ratio λ:1. Then by internal division formula,




3λ = 1



Hence proved that, the origin O divides the line segment joining the points, A(1, –3) and B(–3, 9) in the ratio 1 : 3 internally.


External divison formula:


Coordinates of a point P(x,y) dividing the line segment joining A (x1, y1) and B (x2, y2) in the ratio m:n externally are


Using external division formula,


x =


y =


P (3,–9) is the required point.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Chemical Co-ordination VS Neural Co-ordinationChemical Co-ordination VS Neural Co-ordinationChemical Co-ordination VS Neural Co-ordination48 mins
Some Interesting Proofs in GeometrySome Interesting Proofs in GeometrySome Interesting Proofs in Geometry36 mins
Quiz | Chemical Co-ordinationQuiz | Chemical Co-ordinationQuiz | Chemical Co-ordination47 mins
Quiz | Neural  Co-ordinataionQuiz | Neural  Co-ordinataionQuiz | Neural Co-ordinataion51 mins
Section FormulaSection FormulaSection Formula30 mins
Previous Year RMO QuestionsPrevious Year RMO QuestionsPrevious Year RMO Questions43 mins
NCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in TrianglesKnow About Important Proofs in TrianglesKnow About Important Proofs in Triangles33 mins
Foundation | Human Endocrine SystemFoundation | Human Endocrine SystemFoundation | Human Endocrine System58 mins
Champ Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :