Question 1

22. The ratio in which (4, 5) divides the join of (2, 3)

and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3

Question 2

Let the ratio be m:n

We know

$\boxed{\sf (x,y)=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)}$

$\\ \sf\longmapsto (4,5)=\left((7m+2n)/(m+n),(8m+3n)/(m+n)\right)$

Now

.
$\\ \sf\longmapsto (7m+2n)/(m+n)=4\dots(1)$

$\\ \sf\longmapsto (8m+3n)/(m+n)=5\dots(2)$

Adding both

$\\ \sf\longmapsto (7m+2n+8m+3n)/(m+n)=4+5$

$\\ \sf\longmapsto (7m+8m+2n+3n)/(m+n)=9$

$\\ \sf\longmapsto (15m+5n)/(m+n)=9$

$\\ \sf\longmapsto 15m+5n=9(m+n)$

$\\ \sf\longmapsto 15m+5n=9m+9n$

$\\ \sf\longmapsto 15m-9m=9n-5n$

$\\ \sf\longmapsto 6m=4n$

$\\ \sf\longmapsto (m)/(n)=(6)/(4)$

$\\ \sf\longmapsto (m)/(n)=(3)/(2)$

$\\ \sf\longmapsto m:n=3:2$

Option B is correct

Your comment on this question:

Your answer