Question

Find the ratio in which the line 2x+y=4 divide the join of A(2,-2) and B(3,7).Also find the coordinate of point of divison

Answer 1

The ratio is 2: 3
Explanation:
Let P(x, y) be the point of intersection of
the line 2x + y = 4 and the line joining
A(2, − 2) and B(3, 1),
Assume that P divides line segment AB in
the ration of 1: n,
By section formula,
P(x, y) = ( ,
)
= ( , )
Substituting P(x, y) in 2x + y − 4 = 0,
+ − 4 = 0
⇒ + = 4
⇒ 7 + 2n = 4 + 4n
⇒ 2n = 7 − 4
⇒ n =
Hence, the ratio is 2: 3

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