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Question
The mid-point of the segment AB, as shown in diagram, is C(4, –3). Write down the co-ordinates of A and B.
Solution
Since, point A lies on x-axis, let the co-ordinates of point A be (x, 0).
Since, point B lies on y-axis, let the co-ordinates of point B be (0, y).
Given, mid-point of AB is C(4, −3).
∴ `(4, -3) = ((x + 0)/2, (0 + y)/2)`
`=> (4 - 3) = (x/2, y/2)`
`=> 4 = x/2` and `-3 = y/2`
`=>` x = 8 and y = −6
Thus, the co-ordinates of point A are (8, 0) and the co-ordinates of point B are (0, −6).
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