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Question Number 205596 by cortano12 last updated on 25/Mar/24

Commented by A5T last updated on 25/Mar/24

$$DEisnotuniquelydefined.$$

Answered by TheHoneyCat last updated on 31/Mar/24

$$\mathrm{As}\mathrm{pointed}\mathrm{out}\mathrm{by}A5T\mathrm{this}\mathrm{question}\mathrm{is}\mathrm{missing}$$$$\mathrm{something}\mathrm{to}\mathrm{be}\mathrm{solvable}.$$$$$$$$\mathrm{To}\mathrm{be}\mathrm{more}\mathrm{explicit},\mathrm{you}\mathrm{are}\mathrm{lacking}\mathrm{a}$$$$\mathrm{constraint}\mathrm{on}D.D\mathrm{is}\mathrm{currently}\mathrm{free}\mathrm{to}$$$$\mathrm{be}\mathrm{anywhere}\mathrm{on}\mathrm{the}\mathrm{line},\mathrm{so}x\mathrm{can}\mathrm{take}\mathrm{any}$$$$\mathrm{value}\mathrm{from}+\mathrm{\infty }\left(\mathrm{if}\mathrm{you}\mathrm{send}D\mathrm{to}\mathrm{infinity}\right)$$$$\mathrm{to}1(\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{minial}\mathrm{value}\mathrm{you}\mathrm{can}\mathrm{get}$$$$\mathrm{by}\mathrm{putting}D\mathrm{in}\mathrm{the}\mathrm{middle}\mathrm{of}[C,B].)$$$$$$$$\mathrm{So}\mathrm{the}\mathrm{smartass}\mathrm{answer}\mathrm{is}[1,+\mathrm{\infty }[$$$$\mathrm{but}\mathrm{in}\mathrm{all}\mathrm{seriousness}\mathrm{you}\mathrm{are}\mathrm{missing}\mathrm{a}\mathrm{line}$$$$\mathrm{in}\mathrm{your}\mathrm{exercise}\mathrm{somewhere}...$$

Commented by A5T last updated on 31/Mar/24

$$Theshortestdistancefromapoint,sayE,toa$$$$line,sayBD,isthelengthoftheperpendicular$$$$fromEtoBD.So,tofindtheshortestdistance,$$$$lettheperpendicularfromEtoBDmeetBD$$$$atF.Then,\frac{1}{2}=\frac{EF}{1}(similar△)\Rightarrow EF=\frac{1}{2}.$$

Commented by TheHoneyCat last updated on 31/Mar/24

Oh yeah, my bad ��. Thanks

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