Question

The mid-point of the line segment joining the point $\left(3m,6\right)$ and $\left(-4,3n\right)$ is $(1,2m-1)$. Find $(m,n)$.

• A. $(2,0)$
• B. $(2,2)$
• C. $(0,0)$
• D. $(0,2)$

Answer 1

The correct option is A $(2,0)$

Mid-point of any two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

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

Since $(1,2m-1)$ is midpoint of $(3m,6)$ and $(-4,3n)$, then :

Taking $x$ coordinates,

$1=\frac{3m-4}{2},$

$2=3m-4,$

$3m=4+2$

$3m=6$

$m=2$

Similarly,

Taking $y$ coordinates,

$2m-1=\frac{6+3n}{2},$

$4m-2=6+3n,$

$4\times 2-2=6+3n,$ ($m=2$)

$3n+6=6$

$n=0$

Hence, $(m,n)=(2,0)$