The mid-point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Find the values of a and b.

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Solution

Mid-point of (2a, 4) and (-2, 2b) is (1, 2a + 1), therefore using mid-point formula, we have:

$x equals fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction space space space y equals fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction 1 equals fraction numerator 2 a minus 2 over denominator 2 end fraction space space space space space 2 a plus 1 equals fraction numerator 4 plus 2 b over denominator 2 end fraction 2 equals 2 a minus 2 space space space space space space 4 a plus 2 equals 4 plus 2 b 2 a equals 4 space space space space space space space space space space space space 4 cross times 2 plus 2 equals 4 plus 2 b a equals 2 space space space space space space space space space space space space space space space 10 equals 4 plus 2 b space space space space space space space space space space space space space space space space space space space space space space space space 2 b equals 6 space space space space space space space space space space space space space space space space space space space space space space space space space space b equals 3 T h e r e f o r e space a equals 2 space comma b equals 3$

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