Question

The mid-point of the line segment joining $(a+b-c,2a)$ and $(2a-b+c,2b)$ is $(6,4)$. Then the values of $a$ and $b$ respectively are

• A. 4 and 2
• B. 2 and 4
• C. 4 and 0
• D. 0 and 4

Answer 1

The correct option is C

4 and 0

Given that $(6,4)$ is the mid-point of $(a+b-c,2a)$ and $(2a-b+c,2b)$.

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 $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$\Rightarrow \frac{(a+b-c)+(2a-b+c)}{2}=6$

$⟹\frac{3a}{2}=6$

$\Rightarrow a=4$
Also, $\frac{2a+2b}{2}=4$
$\Rightarrow a+b=4$
Since $a=4$, we have $b=0$
Therefore the values of $a$ and $b$ respectively are 4 and 0.