Question

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

• A. 1:2
• B. 1:3
• C. 2:3
• D. 4:9

Answer 1

Answer:

B. 1:3

I a point divides a line segment in the ratio m:n then the coordinates of the point is

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$A(2,3), B(4,6), C(10,15)$

B divides A and C in the ratio k:1

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$(\frac{k(10)+1(2)}{k+1},\frac{k(15)+1(3)}{k+1})=(4,6)$

$\frac{10k+2}{k+1}=4$

$10k+2=4(k+1)$

$10k+2=4k+4$

$10k-4k=4-2$

$6k=2$

$k=\frac{2}{6}=\frac{1}{3}$