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Question
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
Solution
Suppose the line intersects the y-axis at P(0, y) and the x-axis at Q(x, 0)
It is given that (2, –5) is the mid-point of PQ
Using mid-point formula, we have
`((x+0)/2 , (0+y)/2) = (2, -5)`
`=> (x/2,y/2) = (2, -5)`
`=> x/2 = 2 and y/2 = -5`
`=> x = 4, y = - 10`
Thus, the coordinates of P and Q are (0, −10) and (4, 0), respectively.
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