Question

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

• A. $AP=\frac{1}{3}AB$
• B. $AP=PB$
• C. $PB=\frac{1}{3}AB$
• D. $AP=\frac{1}{4}AB$

Answer 1

The correct option is D $AP=\frac{1}{4}AB$

Given

$A(4,2)B(8,4)andP(2,1)$

use section formula ,

let $PA:PB=m:n$

then,

$2=\frac{8\times m+4\times n}{(m+n)}$

$2(m+n)=(8m+4n)$

$2m+2n=8m+4n$

$-6m=2n$

$\frac{m}{n}=1:-3$

here negative sign means $p$ externally divided of $AB$ .

$AB=AP+BP$

$AB=1AP+3AP$

$4AP=AB$

$AP=\frac{1}{4}AB$