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Question
Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection.
Solution
Let P (-2, y) be the pcint on line x which divides the line segment AB the ratio k : 1.
Coordinates of P are
`- 2 = ("k" - 6)/("k" + 1) ,`
⇒ -2k - 2 = k - 6
⇒ -3k = - 4
⇒ k = `4/3` .....(1)
`=> "k " = 4/3 `
y = `(6"k" - 1)/("k + 1")`
`=> "y" = (69 (4/3) - 1)/(4/3 + 1)` ...from (1)
`=> "y" = (24 - 3)/7 `
⇒ y = 3
Hence, the required ratio is 4: 3 and the point of intersection is (-2, 3).
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