Question

find the ratio in which the straight line3x-4y=7 divides the join of(-2,7) and (-1,3)
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Answer 1

The equation of the line joining the points (1,2) and (2,1) is given by:

1−2

x−1

=

2−1

y−2

∴x+y=3

∴3x+3y=9 ....(1)

And, 3x+4y=7 ....(2) ...Given

Subtracting eq(2) from eq(1), we get

y=−2

Substitute y=−2 in eq(2), we get

x=5

Therefore, the given line cuts the line joining the given points at (5,−2), externally.

By section formula for external division,

x=

m−n

mx

2

−nx

1

⇒5=

m−n

m2−n1

⇒5m−5n=2m−n

⇒3m=4n

⇒m:n=4:3