The mid point of the segment joining $(2 a, 4)$ and $(- 2, 2 b)$ is $(1, 2 a + 1)$ , then value of b is

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Solution

The correct option is C $3$
Mid point of two points ${(x}_{1}, y_{1})$ and ${(x}_{2}, y_{2})$ is calculated by the formula $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$
Given, midpoint of $(2 a, 4)$ and $(- 2, 2 b) = (1, 2 a + 1)$
$=> (\frac{2 a - 2}{2}, \frac{4 + 2 b}{2}) = (1, 2 a + 1)$
$=> \frac{2 a - 2}{2} = 1; \frac{4 + 2 b}{2} = 2 a + 1$
$=> 2 a - 2 = 2; 4 + 2 b = 4 a + 2$
$=> a = 2$
So, $4 + 2 b = 8 + 2$
$=> 4 + 2 b = 10$
$=> 2 b = 6$
$b = 3$

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