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Category: Coordinate Geometry

show-that-the-area-of-the-triangle-whose-vertics-area-0-0-0-x-1-y-1-z-1-x-2-y-2-z-2-is-1-2-y-1-z-2-y-2-z-1-2-

Question Number 49466 by munnabhai455111@gmail.com last updated on 07/Dec/18 $${show}\:{that}\:{the}\:{area}\:{of}\:{the}\:{triangle}\:{whose}\:{vertics}\:{area}\:\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)\:,\:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} ,{z}_{\mathrm{1}} \right)\:,\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2},} {z}_{\mathrm{2}} \right)\:{is}\:\mathrm{1}/\mathrm{2}\left(\sqrt{\Sigma\left({y}_{\mathrm{1}} {z}_{\mathrm{2}} −{y}_{\mathrm{2}} {z}_{\mathrm{1}} \right)^{\mathrm{2}} \:.}\right. \\ $$ Terms of…

Question-49020

Question Number 49020 by ajfour last updated on 01/Dec/18 Commented by ajfour last updated on 01/Dec/18 $${If}\:{the}\:{inscribed}\:{ellipse}\:{is}\:{of}\:{maximum} \\ $$$${area}\:{with}\:{its}\:{major}\:{axis}\:{parallel}\:{to} \\ $$$${side}\:{PQ}\:{of}\:\bigtriangleup{PQR}\:{with}\:{PR}\:=\:{q}\:{and} \\ $$$${QR}\:={p}\:,\:{find}\:\boldsymbol{{a}},\:\boldsymbol{{b}}\:{of}\:{the}\:{ellipse}. \\ $$…

Find-the-area-of-the-triangle-in-the-first-quadrant-between-the-x-and-y-axis-and-the-tangent-to-the-relationship-curve-y-5-x-x-5-and-x-dont-equal-0-at-0-5-

Question Number 179458 by cortano1 last updated on 29/Oct/22 $$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{quadrant}\:\mathrm{between}\:\mathrm{the}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{relationship}\:\mathrm{curve}\:\mathrm{y}=\frac{\mathrm{5}}{\mathrm{x}}−\frac{\mathrm{x}}{\mathrm{5}}\:\mathrm{and}\:\mathrm{x}\:\mathrm{dont} \\ $$$$\mathrm{equal}\:\mathrm{0}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{5}\right) \\ $$ Commented by Acem…

Donnes-AD-1-DB-6-BCD-45-BAC-90-Determiner-1-AC-2-AE-Solution-BAC-BAC-90-BC-2-AB-2-AC-2-CD-cote-commun-aux-BAC-et-BDC-DB-2-CD-2-BC-2-2BC-CDcos-45-1-

Question Number 179360 by a.lgnaoui last updated on 28/Oct/22 $${Donnes}:\:\mathrm{AD}=\mathrm{1};\:\mathrm{DB}=\mathrm{6};\:\measuredangle{BCD}=\mathrm{45}°\:;\:\measuredangle{BAC}=\mathrm{90}° \\ $$$${Determiner} \\ $$$$\left.\mathrm{1}\right)\:\:\mathrm{A}{C}\:\:?\:\: \\ $$$$\left.\mathrm{2}\right)\:\:\mathrm{A}{E}? \\ $$$$−−−−−−−−−−−− \\ $$$${Solution} \\ $$$$\bigtriangleup{BAC}\:\:\:\:\:\:\measuredangle{BAC}=\mathrm{90}° \\ $$$${BC}^{\mathrm{2}} ={AB}^{\mathrm{2}}…