Question

Find the value of $k$, so that $(2,1)$ is the midpoint between $(1,k)$ and $(3,1)$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

We know the midpoint of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$is given as
$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
Substitute the values, we get
$(\frac{1+3}{2},\frac{k+1}{2})$ $=$ $(2,1)$
On equating, we get
$\left(\frac{k+1}{2}\right)$ $=1$
$\Rightarrow k+1=2$
$\Rightarrow k=2-1$
$\Rightarrow k=1$