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Question Number 209398 by SonGoku last updated on 09/Jul/24

Is it possible to determine the points A(x_1 , y_1 ) and  B(x_2 , y_2 ) knowing that the distance between them is  2(√(29))?

$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{points}\:\mathrm{A}\left(\mathrm{x}_{\mathrm{1}} ,\:\mathrm{y}_{\mathrm{1}} \right)\:\mathrm{and} \\ $$$$\mathrm{B}\left(\mathrm{x}_{\mathrm{2}} ,\:\mathrm{y}_{\mathrm{2}} \right)\:\mathrm{knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them}\:\mathrm{is} \\ $$$$\mathrm{2}\sqrt{\mathrm{29}}? \\ $$

Answered by Frix last updated on 09/Jul/24

How should this be possible?  ∣AB∣=(√((x_1 −x_2 )^2 +(y_1 −y_2 )^2 ))=2(√(29))  This is a formula for all circles in R^2  with  radius 2(√(29))...

$$\mathrm{How}\:\mathrm{should}\:\mathrm{this}\:\mathrm{be}\:\mathrm{possible}? \\ $$$$\mid{AB}\mid=\sqrt{\left({x}_{\mathrm{1}} −{x}_{\mathrm{2}} \right)^{\mathrm{2}} +\left({y}_{\mathrm{1}} −{y}_{\mathrm{2}} \right)^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{29}} \\ $$$$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{formula}\:\mathrm{for}\:{all}\:\mathrm{circles}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{with} \\ $$$$\mathrm{radius}\:\mathrm{2}\sqrt{\mathrm{29}}... \\ $$

Commented by SonGoku last updated on 09/Jul/24

But how do I define x_1 , y_1 , x_2  and y_2  with only thet  informaion of the distance 2(√(29))?

$$\mathrm{But}\:\mathrm{how}\:\mathrm{do}\:\mathrm{I}\:\mathrm{define}\:\mathrm{x}_{\mathrm{1}} ,\:\mathrm{y}_{\mathrm{1}} ,\:\mathrm{x}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}_{\mathrm{2}} \:\mathrm{with}\:\mathrm{only}\:\mathrm{thet} \\ $$$$\mathrm{informaion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{2}\sqrt{\mathrm{29}}? \\ $$

Commented by Frix last updated on 09/Jul/24

You cannot.

$$\mathrm{You}\:\mathrm{cannot}. \\ $$

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