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In what ratio does the line x-y-2 = 0 divides the line segment joining (3, -1) and (8, 9)?

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ANSWER


3: 2

Step-by-step explanation

The equation of the line connecting (3,-1) and (8,9) is


y - 2x = - 7...(1)

The given line segment also have equation


x - y - 2 = 0

Or


x - y = 2..(2)

Adding equation (2) and (1) gives,


- x = - 5


x = 5

We substitute x=5 into equation (2) to get,


5 - y = 2


y = 3

This means that the point of intersection is (5,3)

Let this point divide the line segment joining (3, -1) and (8, 9) in the ratio

m:n

Then,


(3m + 8n)/(m + n) = 5

This implies that,


5m + 5n = 3m + 8n


2m = 3n


(m)/(n) = (3)/(2)

m:n=3:2

User Kostas Dimakis
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