Question #3c7bb

1 Answer
Dec 20, 2017

Answer:

# 2/7," from "(-5,11)#.

Explanation:

Suppose that, #P(-3,7)# divide, in the ratio #lambda,# the join of

#A(-5,11) and B(4,-7)# from #A#.

Then, by the Section Formula, #P# must be,

#P((4lambda-5)/(lambda+1),(-7lambda+11)/(lambda+1))#.

Since, #P=P(-3,7),# we have,

#(4lambda-5)/(lambda+1)=-3, &, (-7lambda+11)/(lambda+1)=7#.

#:. 4lambda-5=-3lambda-3, &, -7lambda+11=7lambda+7#.

#:. 7lambda=2, and, -14lambda=-4#.

#:. lambda=2/7, and, lambda=(-4)/(-14)=2/7#, is the desired ratio.