Question

If $z=\frac{m{z}_1+z_2}{m+1}$, then distance of point $z$ from the line joining $z_1+1$ and $z_2+1$ is

• A. $0$
• B. $1$
• C. $\frac{2m}{m+1}$
• D. $\frac{m}{m+1}$

Answer 1

Answer: (B)

$1$

$z=\frac{m{z}_1+z_2}{m+1}$

$\Rightarrow z_1+1,z_2+1=?$

$\Rightarrow z=\frac{\left(m\right)z_1+\left(1\right)z_1}{m+1}$

Its of the ratio $m:1.$

$m:1$ divides the line $(z_1+1)$ and $(z_2+1).$

Then the distance of point $z$ from the line joining $=1.$