Question

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

• A. a = 2, b = 3
• B. a = 3, b = 2
• C. a = 4, b = 3
• D. a = 3, b = 4

Answer 1

The correct option is A

a = 2, b = 3

Given that (1, 2a + 1) is the mid - point of (2a, 4) and (-2, 2b).

We know that mid-point of the line joining two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$\therefore \frac{2a-2}{2}=1\Rightarrow 2a=4\Rightarrow a=2$

Also, $\frac{4+2b}{2}=2a+1$
$\Rightarrow 4+2b=4a+2$
$\Rightarrow 2b=4a-2$
$\Rightarrow 2b=8-2$
$\Rightarrow b=\frac{6}{2}=3$

Hence, $a=2$ and $b=3$