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प्रश्न
Find the ratio in which the point P (2, 4) divides the line joining points (-3, 1) and (7, 6).
उत्तर
Let the point P divides AB in the ratio k : 1.
Coordinates of P are
x = `(7"k" - 3)/("k" + 1)`
y = `(6"k" + 1)/("k" + 1)`
But given, P(x, y) =P(2, 4)
`therefore 2 = (7"k" - 3)/("k" + 1)`
⇒ 2k + 2 = 7k - 3
⇒ 5 = 5k
⇒ k = 1
k : 1 = 1 : 1
or `4 = (6"k" + 1)/("k" + 1)`
4k + 4 = 6k + 1
⇒ 3 = 2k
⇒ k = `3/2`
k : 1=3 : 2
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