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5 votes
5 votes
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


User Shehabul Alam
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1 Answer

15 votes
15 votes

Let the ratio be m:n

  • (x,y)=(4,5)
  • Points be (x1,y1)=(2,3)
  • (x2,y2)=(7,8)

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

User Pmjobin
by
3.5k points