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Question Number 33217 by Tinkutara last updated on 13/Apr/18

Commented by Rasheed.Sindhi last updated on 13/Apr/18

$$\mathrm{N}=2?$$$$(\mathrm{I}\mathrm{supposed}\mathrm{that}\mathrm{both}\mathrm{cordinates}\mathrm{of}\mathrm{mid}-$$$$\mathrm{points}\mathrm{be}\mathrm{not}\mathrm{integer}.)$$

Commented by Tinkutara last updated on 13/Apr/18

I don't have answer in my book. I found 3 points.

Commented by Rasheed.Sindhi last updated on 13/Apr/18

$$\mathrm{Any}\mathrm{three}\mathrm{points}\mathrm{for}\mathrm{example}?$$

Commented by Tinkutara last updated on 14/Apr/18

$$(0,0),(1,3)(3,4)$$

Commented by Rasheed.Sindhi last updated on 14/Apr/18

$$(0,0),(1,3),(3,4)\mathrm{\&}(6,5)$$$$\mathrm{e}=\mathrm{even}\mathrm{\&}\mathrm{o}=\mathrm{odd}$$$$(\mathrm{e},\mathrm{e}),(\mathrm{e},\mathrm{o}),(\mathrm{o},\mathrm{o}),(\mathrm{o},\mathrm{e})\mathrm{are}\mathrm{required}\mathrm{points}.$$$$(\mathrm{e},\mathrm{e}),(\mathrm{e},\mathrm{o})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{e}+\mathrm{e}}{2},\frac{\mathrm{e}+\mathrm{o}}{2})$$$$(\mathrm{e},\mathrm{e}),(\mathrm{o},\mathrm{o})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{e}+\mathrm{o}}{2},\frac{\mathrm{e}+\mathrm{o}}{2})$$$$(\mathrm{e},\mathrm{e}),(\mathrm{o},\mathrm{e})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{e}+\mathrm{o}}{2},\frac{\mathrm{e}+\mathrm{e}}{2})$$$$(\mathrm{e},\mathrm{o}),(\mathrm{o},\mathrm{o})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{e}+\mathrm{o}}{2},\frac{\mathrm{o}+\mathrm{o}}{2})$$$$(\mathrm{e},\mathrm{o}),(\mathrm{o},\mathrm{e})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{e}+\mathrm{o}}{2},\frac{\mathrm{o}+\mathrm{e}}{2})$$$$(\mathrm{o},\mathrm{o}),(\mathrm{o},\mathrm{e})\Rightarrow \mathrm{midpoint}=(\frac{\mathrm{o}+\mathrm{o}}{2},\frac{\mathrm{o}+\mathrm{e}}{2})$$$$\mathrm{written}\mathrm{in}\mathrm{red}\mathrm{are}\mathrm{not}\mathrm{integers}.$$$$-------------$$$$\mathrm{e}+\mathrm{e}=\mathrm{e}\Rightarrow \frac{\mathrm{e}+\mathrm{e}}{2}\mathrm{is}\mathrm{integer}$$$$\mathrm{o}+\mathrm{o}=\mathrm{e}\Rightarrow \frac{\mathrm{o}+\mathrm{o}}{2}\mathrm{is}\mathrm{integer}$$$$\mathrm{e}+\mathrm{o}=\mathrm{o}\Rightarrow \frac{\mathrm{e}+\mathrm{o}}{2}\mathrm{is}\mathrm{not}\mathrm{integer}$$$$\mathrm{o}+\mathrm{e}=\mathrm{o}\Rightarrow \frac{\mathrm{o}+\mathrm{e}}{2}\mathrm{is}\mathrm{not}\mathrm{integer}$$

Commented by Rasheed.Sindhi last updated on 14/Apr/18

$$\mathrm{If}\mathrm{we}\mathrm{mean}\mathrm{by}‘‘\mathrm{does}\mathrm{not}\mathrm{have}\mathrm{integer}{\mathrm{coordinates}}^{″}$$$$\mathrm{both}\mathrm{coordinates}\mathrm{non}-\mathrm{integer},\mathrm{then}\mathrm{N}=2$$$$(\mathrm{e},\mathrm{e}),(\mathrm{o},\mathrm{o})or(\mathrm{e},\mathrm{o}),(\mathrm{o},\mathrm{e})$$

Commented by Tinkutara last updated on 14/Apr/18

Thank you very much Sir! I got the answer. ��������

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