z = (1 – t)z₁ + tz₂

z = z₁ + t(z₂ – z₁)

z – z1 = t(z₂ – z₁)            .....(1)

  $\therefore$         | z – z₁ | + | z – z2 | = | z₁ – z₂ |              $\therefore$         A is correct

                Arg (z – z₁) + arg (z – z₂) = p                 $\therefore$         B is incorrect

                Arg (z – z₁) = Arg(z₂ – z1)                      $\therefore$         D is correct

            from (1)           $\overline{\mathrm{z}}-{\overline{\mathrm{z}}}_1=\mathrm{t}({\overline{\mathrm{z}}}_2-{\overline{\mathrm{z}}}_2)$            .....(2)

 $\therefore \frac{\mathrm{z}-{\mathrm{z}}_1}{{\mathrm{z}}_2-{\mathrm{z}}_1}=\frac{\overline{\mathrm{z}}-{\overline{\mathrm{z}}}_1}{{\overline{\mathrm{z}}}_2-{\overline{\mathrm{z}}}_1}$

 $\therefore \left|\begin{array}{cc}z-z_1& \overline{z}-{\overline{z}}_1\\ z_2-z_1& {\overline{z}}_2-{\overline{z}}_1\end{array}\right|=0$                                $\therefore$         C is correct