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Question Number 200412 by hardmath last updated on 18/Nov/23

$$\mathrm{If}$$$$\sqrt{{(\mathrm{x}-6)}^2+{(\mathrm{y}+1)}^2}+\sqrt{{(\mathrm{x}-9)}^2+{(\mathrm{y}+5)}^2}$$$$$$$$\mathrm{find}:\mathrm{minumum}=?$$

Answered by witcher3 last updated on 18/Nov/23

$$\mathrm{A}(6,-1);\mathrm{B}=(9,-5)$$$$\mathrm{M}(\mathrm{x},\mathrm{y})$$$$\mathrm{we}\mathrm{want}\min \mathrm{AM}+\mathrm{MB}⩾\mathrm{AB};\mathrm{\forall }\mathrm{M}\in {\mathrm{IR}}^2$$$$\mathrm{AM}+\mathrm{MB}=\mathrm{AB},\mathrm{\forall }\mathrm{M}\in \left[\mathrm{AB}\right]$$$$\min =\sqrt{{(6-9)}^2+{(-1+5)}^2}=\sqrt{9+16}=5$$

Commented by hardmath last updated on 18/Nov/23

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

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