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Question
The line segment joining A(4, 7) and B(−6, −2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.
Solution
Since, point K lies on y-axis, its abscissa is 0.
Let the point K (0, y) divides AB in the ratio k : 1
We have,
`x = (k xx (-6) + 1 xx 4)/(k + 1)`
`0 = (-6k + 4)/(k + 1)`
`k = 4/6 = 2/3`
Thus, K divides AB in the ratio 2 : 3.
Also, we have:
`y = (k xx (-2) + 1 xx 7)/(k + 1)`
`y = (-2k + 7)/(k + 1)`
`y = (-2 xx 2/3 + 7)/(2/3 + 1)`
`y = (-4 + 21)/(2 + 3)`
`y = 17/5`
Thus, the co-ordinates of the point K are `(0, 17/5)`
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