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Question
Find the ratio in which the line y = -1 divides the line segment joining (6, 5) and (-2, -11). Find the coordinates of the point of intersection.
Solution
Let R (x, -1) be the point on the line y = - 1 which divides the line segment PQ in the ratio k: 1.
Coordinates of R are,
x = `(2"k" + 6)/("k" + 1) ,` -1 = `(-11 "k" + 5)/("k" + 1)`
x = `(-2 (3/5) + 6)/(3/5 + 1), => - "k" - 1 = - 11 "k" + 5`
`=> "x" = (-6 + 30)/8 => 10 "k" = 6`
x = 3 ⇒ k = 3/5 .....(1)
Hence, the required ratio is 3: 5 and the point of inter sec tion is (3, - 1).
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