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प्रश्न
The line 7x - 8y = 4 divides join of (-8,-4) and (6,k) in the ratio of 2 : 5. Find the value of k.
उत्तर
Let the point of intersection of AB and the line 7x-8y=4, be the point P (a,b)
Also, given the line 7x-8y = 4 divides the line segment AB in the ratio 2 : 5.
i.e. AP: PB = 2: 5
Coordinates of P are,
P (a,b) = P `((12 - 40)/7 , (2"k" - 20)/7) = "P" (-4, (2"k" - 20)/7)`
P (a,b) lies on the line 7x - 8y = 4,
P will satisfy the equation of the line
7(-4) - `((2"k" - 20)/7)` = 4
-8 `((2"k" - 20)/7)` = 32
2k - 20 = -28
2k = -8
k = -4
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