Question

If A(2,3) , B(4,6), C(10,15) are three collinear points, then B divides the line segment joining A , C in the ratio:

• A. 1:2
• B. 2:1
• C. 3:1
• D. 1:3

Answer 1

Answer:

D. 1:3

$x_1=2,y_1=3,x_2=10,y_2=15,x=4,y=6$

$B(4,6)=(\frac{10m+2n}{m+n},\frac{15m+3n}{m+n})$

$\frac{10n+2n}{m+n}=4$

$10m+2n=4m+4n$

$6m=2n$

$\frac{m}{n}=\frac{2}{6}=\frac{1}{3}$

$\frac{15m+3n}{m+n}=6$

$15m+3n=6m+6n$

$9m=3n$

$\frac{m}{n}={3}{9}=\frac{1}{3}$