Find the ratio in which the staight line 5x+4y=4 divides the join of (4,5) and (7,-1)?

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Answer 1 · 2017-08-12T10:30:17

# -16/27.#

Let, #A=A(4,5) and B=B(7,-1),# be the given pts.

Suppose that, the given line, say, #L : 5x+4y=4......(ast),#

divides, from #A,# the line sgmt. #AB,# in the ratio #lambda:1# in the pt. #P.#

Using the Section Formula, the co-ords. of the pt. #P# are,

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

But, as #P in L,# we see that the co-ords. of #P# must satisfy #(ast).#

#:. 5((7lambda+4)/(lambda+1))+4((-1lambda+5)/(lambda+1))=4.#

#:. 35lambda+20-4lambda+20=4lambda+4,#

#:. 27lambda=-16," giving, "#

# lambda=-16/27,# the desired Ratio.