Question

If point $R(X,Y)$ is mid point of the line joining $P(X,Y)$ and $Q(x_2,y_2)$ internally and $m_1=m_2$, then the coordinates of R are

• A. $x_1+x_2,y_1+y_2$
• B. $\left(\begin{array}{c}\frac{x_1+x_2}{2}\end{array}\right),\left(\begin{array}{c}\frac{y_1+y_2}{2}\end{array}\right)$
• C. $2(x_1+x_2),2(y_1+y_2)$
• D. None of the above

Answer 1

Answer: (B)

$\left(\begin{array}{c}\frac{x_1+x_2}{2}\end{array}\right),\left(\begin{array}{c}\frac{y_1+y_2}{2}\end{array}\right)$

By section formula for internal division,

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$ and $y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

where, $m_1=1,m_2=1$

$\therefore x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

So, option B is correct.