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Question
Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.
Solution
Let C(x, 0) divides the line-segment A(1, –3) and B(4, 5) in k : 1 ratio.
By section formula,
`(x, y ) = ((mx_2 + nx_1)/(m+n), (my_2 + ny_2)/(m +n))`
⇒ `(x,0) = ((4k + 1xx1)/(k + 1) , (5k + 1 xx (-3))/(k + 1))`
⇒ `(x , 0) = ((4k + 1)/(k + 1) , (5k - 3)/(k + 1))`
⇒ `(5k - 3)/(k + 1) = 0`
⇒ `5k - 3 = 0`
⇒ `5k = 3`
⇒ `k = (3)/(5)`
and `x = (4k + 1)/(k + 1) = (4 xx (3)/(5) +1)/((3)/(5)+1)`
⇒ `x = ((12+5)/(5))/((3+5)/(5))`
⇒ `x = (17)/(8)`
The ratio in which C divides A and B is k : 1 i.e., 3 : 5 and the coordinate of C is `((17)/(8) , 0)`.
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