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

X = (m1x2 + m2x1)/ m1 + m2


= (1 × (– 2) + 1× 2a)/1 + 1


= (– 2 + 2a) /2


(– 2 + 2a)/2 = 1


– 2 + 2a = 2


2a = 4


a = 2


Y = (m1y2 + m2y1)/ m1 + m2


= (1 × 3b + 1 ×4)/2


= (3b + 4)/2


(3b + 4)/2 = 2a + 1


(3b + 4)/2 = 5


(3b + 4) = 10


3b = 6


b = 2


a = 2, b = 2


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