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Question
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
Options
1 : 3
2 : 3
3 : 1
2 : 3
Solution
3 : 1
Explanation:
Let P(0, y) be the point of intersection of y-axis with the line segment joining A (−3,−4) and B (1, −2) which divides the line segment AB in the ratio λ : 1.
Now according to the section formula if point a point P divides a line segment joining` A (x_1, y_1) "and" B (x_2, y_2)` in the ratio m : n internally than,
`P(x , y ) = ((nx_1+mx_2)/(m+n) , (ny_1+my_2)/(m+n))`
Now we will use section formula as,
`(0 , y) = ((lambda -3)/(lambda + 1) , (-2lambda -4)/(lambda+1))`
Now equate the x component on both the sides,
`(lambda - 3 ) /(lambda +1) = 0`
On further simplification,
`lambda = 3`
So y-axis divides AB in the ratio `3/1`.
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