Question

FInd ThE RatIo In WhicH ThE LiNE Segment JoiNIng(-2,-3)AND(5,6) Is DiViDed By (1) X-AxiS. (2) Y- AxiS.ALso,Find The CoorDInATeS Of ThE PoINt Of DiVisIOn In EacH CaSe

Answer 1

1) Let the coordinate of the point of division is (a,0). If the ratio is m:n then
a=(5m-2n)/(m+n) ------------ (i) and
0=(6m-3n)/(m+n)
or, 6m-3n=0
or, 6m=3n
or, m/n=3/6
or, m/n=1/2
Putting n (i) -
a=(5.1-2.2)/(1+2)
=(5-4)/3
=1/3
∴, the required ration is 1:2 and the coordinate of the point of division is (1/3,0). Ans.
2) Let the coordinate of the point of division is (0,b). If the ratio is m':n' then
0=(5m'-3n')/(m'+n')
or, 5m'-3n'=0
or, 5m'=3n'
or, m'/n'=3/5 and
b=(3.6-5.3)/(3+5)
=(18-15)/8
=3/8
∴, the required ration is 3:5 and the coordinate of the point of division is (0,3/8) Ans.