Straight Line Question 114

Question: In what ratio the line $ y-x+2=0 $ divides the line joining the points (3, -1) and (8, 9) [Karnataka CET 2002]

Options:

A) 1 : 2

B) 2 : 1

C) 2 : 3

D) 3 : 4

Show Answer

Answer:

Correct Answer: C

Solution:

  • Given, equation of line $ y-x+2=0 $ and co-ordinates of points $ (x_1,y_1)=(3,-1) $ and $ (x_2,y_2)=(8,9) $ . We know that if the ratio in which a line $ ax+by+c=0 $ is divided by points $ (x_1,y_1) $ and $ (x_2,y_2) $ is $ \lambda :1 $ , then intersecting point $ ( \frac{\lambda x_2+x_1}{\lambda +1},\frac{\lambda y_2+y_1}{\lambda +1} ) $ lies on $ ax+by+c=0 $ . Thus any point on the line joining $ (3,-1) $ and $ (8,9) $ dividing it in the ratio $ \lambda :1 $ is $ ( \frac{8\lambda +3}{\lambda +1},\frac{9\lambda -1}{\lambda +1} ) $ and if it lies on $ y-x+2=0, $ then $ \frac{9\lambda -1}{\lambda +1}-\frac{8\lambda +3}{\lambda +1}+2=0 $ or $ 9\lambda -1-(8\lambda +3)+2(\lambda +1)=0 $ or $ 3\lambda -2=0,\lambda =\frac{2}{3} $ i.e. ratio is $ 2:3 $ .

Engineering Preparation

Physics 11th

Physics 12th

Chemistry 11th

Chemistry 12th

Mathematics 11th

Mathematics 12th

JEE Previous Year Questions

JEE Tutorial Sessions

Medical Preparation

Physics 11th

Physics 12th

Chemistry 11th

Chemistry 12th

Biology 11th

Biology 12th

NEET Previous Year Questions

NEET Tutorial Sessions

NCERT Books & Solutions

NCERT Books for JEE

NCERT Books for NEET

NCERT Solutions for JEE

NCERT Solutions for NEET

NCERT Exemplar for JEE

NCERT Exemplar for NEET

Important Resources

Physics Formulas

Chemistry Formulas

Mathematics Formulas

JEE Articles

NEET Articles

Other Resources

Media Coverage

Help Videos

Current Affair

Student Help Booklet

SPOC Help Booklet

Syllabus

JEE Syllabus

NEET Syllabus

Mentorship

Mentorship for JEE

Mentorship for NEET

NCERT Exemplar Video Solutions

NCERT Exercise Video Solution

icon  BETA

© 2014-2025 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in
Media coverage of SATHEE
goolge

Play Store
goolge

App Store
The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.