The midpoint of the line segment A(2a, 4) and B(-2, 3b) is C(1, 2a+1). Find the values of a and b.

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Solution

$w h e n space P open parentheses x comma y close parentheses space b e space t h e space m i d space p o i n t space o f space Q open parentheses x subscript 1 comma y subscript 1 close parentheses space a n d space R open parentheses x subscript 2 comma y subscript 2 close parentheses t h e n open parentheses x comma y close parentheses equals open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses i n space t h i s space q u e s t i o n x equals 1 comma y equals 2 a plus 1 comma x subscript 1 equals 2 a comma y subscript 1 equals 4 comma x subscript 2 equals negative 2 comma y subscript 2 equals 3 b t h e n open parentheses 1 comma 2 a plus 1 close parentheses equals open parentheses fraction numerator 2 a minus 2 over denominator 2 end fraction comma fraction numerator 4 plus 3 b over denominator 2 end fraction close parentheses t h e n 1 equals fraction numerator 2 a minus 2 over denominator 2 end fraction 2 equals 2 a minus 2 2 a equals 4 a equals 2 a n d 2 a plus 1 equals fraction numerator 4 plus 3 b over denominator 2 end fraction w e space g e t space a equals 2 5 equals fraction numerator 4 plus 3 b over denominator 2 end fraction 10 equals 4 plus 3 b 3 b equals 6 b equals 2 s o a equals 2 space & b equals 2$

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