Question

If the midpoint of join of $(x,y+1)$ and $(x+1,y+2)$ is $\left(\frac{3}{2},\frac{5}{2}\right)$ then the midpoint of join of $(x-1,y+1)$ and $(x+1,y-1)$ is

• A. $\left(-1,-1\right)$
• B. $\left(1,1\right)$
• C. $\left(1,-1\right)$
• D. $\left(-1,1\right)$

Answer 1

The correct option is B

$\left(1,1\right)$

Explanation of the correct option.

Compute the required value.

We know that midpoint $\left(x,y\right)$ of line joining the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by,

$\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Given: $\left(\frac{3}{2},\frac{5}{2}\right)$ is the midpoint of the line joining the points $\left(x,y+1\right)$ and $\left(x+1,y+2\right)$

Thus,

$\begin{array}{rcl}\frac{x+x+1}{2}& =& \frac{3}{2}\\ & \Rightarrow & 2x+1=3\\ & \Rightarrow & x=1\end{array}$

Now

$\begin{array}{rcl}\frac{y+1+y+2}{2}& =& \frac{5}{2}\\ & \Rightarrow & 2y+3=5\\ & \Rightarrow & y=1\end{array}$

Thus the joining points are $\left(0,2\right)$ and $\left(2,0\right)$ .

Therefore, the midpoint $\left(m,n\right)$ of the line joining the points $\left(0,2\right)$ and $\left(2,0\right)$

$$\begin{gathered} \left(m,n\right)=\left(\frac{0+2}{2}.\frac{2+0}{2}\right) \\ \Rightarrow \left(m,n\right)=\left(1,1\right) \end{gathered}$$

Hence option $\left(B\right)$ is the correct option.