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Question
The line segment joining A (2, 3) and B (6, –5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.
Solution
Since, point K lies on x-axis, its ordinate is 0.
Let the point K (x, 0) divides AB in the ratio k : 1.
We have,
`y = (k xx (-5) + 1 xx 3)/(k + 1)`
`0 = (-5k + 3)/(k + 1)`
`k = 3/5`
Thus, K divides AB in the ratio 3 : 5.
Also, we have:
`x = (k xx 6 + 1 xx 2)/(k + 1)`
`x = (3/5 xx 6 + 2)/(3/5 + 1)`
`x = (18 + 10)/(3 + 5)`
`x = 28/8 = 7/2 = 3 1/2`
Thus, the co-ordinates of the point K are `(3 1/2, 0)`.
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