Question

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

• A. 4 and 5
• B. 3 and 5
• C. 2 and 3
• D. 1 and 2

Answer 1

The correct option is C

2 and 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, $\frac{4+2b}{2}=2a+1$
$\Rightarrow 4+2b=4a+2$
$\Rightarrow 2b=4a-2$
Since $a=2$, we have $b=3$
Hence, $a=2$ and $b=3$