If-P-2-1-and-A-and-B-lie-on-x-axis-and-y-x-respectively-such-that-PA-PB-AB-is-minimum-find-A-and-B-

Question Number 18823 by rish@bh last updated on 30/Jul/17

$$\mathrm{If}\:\mathrm{P}\equiv\left(\mathrm{2},\mathrm{1}\right)\:\mathrm{and}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{x}−\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{y}=\mathrm{x}\:\mathrm{respectively}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{PA}+\mathrm{PB}+\mathrm{AB}\:\mathrm{is}\:\mathrm{minimum}\:\mathrm{find} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$

Commented by ajfour last updated on 30/Jul/17

$$\mathrm{just}\:\mathrm{guessing}\:\mathrm{only}. \\ $$

Commented by ajfour last updated on 30/Jul/17

$$\mathrm{A}\equiv\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{3}},\:\mathrm{0}\right)\: \\ $$$$\mathrm{B}\equiv\left(\frac{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}},\frac{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}\right) \\ $$

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