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Question
The mid point of the line segment joining (4a, 2b – 3) and (−4, 3b) is (2, –2a). Find the values of a and b.
Solution
It is given that the mid-point of the line segment joining (4a, 2b – 3) and (−4, 3b) is (2, –2a).
∴ `(2, -2a) = ((4a - 4)/2,(2b - 3 + 3b)/2)`
`=> 2 = ((4a - 4)/2)`
`=>` 4a − 4 = 4
`=>` 4a = 8
`=>` a = 2
Also,
`-2a = (2b - 3 + 3b)/2`
`=> -2 xx 2 = (5b - 3)/2`
`=>` 5b − 3 = −8
`=>` 5b = −5
`=>` b = −1
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