Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4),then (A) AP = 1/3 AB (B) AP =1/3 PB (C) (D)

If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4),then

 \\(A) \mathrm{AP}=\frac{1}{3} \mathrm{AB} \\(B) \mathrm{AP}=1 / 3 \mathrm{~PB} \\(C) \mathrm{PB}=\frac{1}{3} \mathrm{AB} \\(D) \mathrm{AP}=\frac{1}{2} \mathrm{AB}

 

Answers (1)

Let P divide  A B  in ratio  k: 1 
\\\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(4,2) \quad\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(8,4)\\P=\left(\frac{k(8)+1(4)}{k+1}, \frac{k(4)+1(2)}{k+1}\right)
By using section formula
Here,

\mathrm{P}=(2,1)
(2,1)=\left(\frac{8 k+4}{k+1}, \frac{4 k+12}{k+1}\right)
Compare x co-ordinate
\\\frac{8 k+4}{k+1}=2 \\8 k+4=2 k+2 \\6 k=-2 \\k=\frac{-2}{6}=\frac{-1}{3} \\Here, k is negative. Hence P divides A B in ratio 1: 3 externally. \\\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{1}{3}$ \\$\mathrm{AP}=\frac{1}{3} \mathrm{~PB}

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question