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Question Number 19506 by Tinkutara last updated on 12/Aug/17

$$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{line}$$$$\mathrm{joining}\mathrm{the}\mathrm{points}{z}_1\mathrm{and}{z}_2\mathrm{can}\mathrm{be}\mathrm{put}$$$$\mathrm{in}\mathrm{the}\mathrm{form}z={tz}_1+(1-t)z_2,\mathrm{where}$$$$t\mathrm{is}\mathrm{a}\mathrm{parameter}.$$

Answered by ajfour last updated on 12/Aug/17

$$\mathrm{z}-{\mathrm{z}}_2=\mathrm{t}({\mathrm{z}}_1-{\mathrm{z}}_2)$$$$\Rightarrow \mathrm{z}={\mathrm{tz}}_1+(1-\mathrm{t}){\mathrm{z}}_2.$$

Commented by Tinkutara last updated on 12/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

Commented by ajfour last updated on 12/Aug/17

$$\mathrm{z},{\mathrm{z}}_1,{\mathrm{z}}_2\mathrm{being}\mathrm{on}\mathrm{the}\mathrm{same}\mathrm{line},$$$$\mathrm{z}-{\mathrm{z}}_2\mathrm{is}\mathrm{parallel}\mathrm{to}{\mathrm{z}}_1-{\mathrm{z}}_2.$$

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