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Question
Find the ratio in which the y-axis divides the line segment joining the points (−4, − 6) and (10, 12). Also find the coordinates of the point of division ?
Solution
Let the y-axis divide the line segment joining the points (−4, −6) and (10, 12) in the ratio λ : 1. and the point of the intersection be (0, y).
So, by section formula, we have:
`((10lambda+(-4))/(lambda+1),(12lambda+(-6))/(lambda+1))=(0,y)`
`therefore(10lambda+(-4))/(lambda+1)=0rArr10lambda-4=0`
`rArrlambda=4/10=2/5`
`thereforey=(12lambda+(-6))/(lambda+1)=(12xx2/5-6)/(2/5+1)=((24-30/5))/((2+5)/5)`
Thus, the y-axis divides the line segment joining the given points in the ratio 2 : 5 and the point of division is`(0,-6/7)`
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