Question

find the ratio which line 3x +4y -9=0 divides the point (1,3) (2,7)

Answer 1

let the required ration be K:1
then section formula :-
mx
$mx \binom{}{2} + nx \binom{}{1 } \div m + n$
here m=k and n=1
now x
x1= 1 y1=3
x2= 2 y2=7

k×2+1×1÷k+1 its for x coordinate


now for y coordinate
k×7+1×3÷k+1


(2k+1/k+1) , (7k+3/k+1) now put these value in the eq 3x+4y-9=0
3(2k+1/k+1)+4(7k+3/k+1)=9
6k+3+28k+12=9k+9
34k+15=9k+9
34k-9k=-15+9
25k=-6
k=-6/25