Question Number 153479 by naka3546 last updated on 07/Sep/21
$${Find}\:\:{area}\:\:{of}\:\:{region}\:\:{that}\:\:{satisfy}\:\: \\ $$$$\:\:\:\mid{x}−\mathrm{2}\mid\:+\:\mid{y}+\mathrm{3}\mid\:<\:\mathrm{3} \\ $$
Answered by aleks041103 last updated on 07/Sep/21
$${Translation}\:{doesn}'{t}\:{change}\:{the}\:{region}'{s} \\ $$$${area}.\:{Therefore}\:{we}\:{can}\:{find}\:{the}\:{area} \\ $$$${of}\:{the}\:{region}\:\mid{x}\mid+\mid{y}\mid<\mathrm{3}\:{instead}. \\ $$$${The}\:{boundary}\:{is} \\ $$$$\mid{x}\mid+\mid{y}\mid=\mathrm{3} \\ $$$$\mathrm{1}{st}\:{quadrant}:\:{y}=\mathrm{3}−{x} \\ $$$$\mathrm{2}{nd}\:{quadrant}:\:{y}={x}−\mathrm{3} \\ $$$$\mathrm{3}{rd}\:{quadrant}:\:{y}=−\mathrm{3}−{x} \\ $$$$\mathrm{4}{th}\:{quadrant}:\:{y}=\mathrm{3}+{x} \\ $$$$ \\ $$$${Then}\:{the}\:{area}\:{is}\:{simply} \\ $$$${A}=\mathrm{4}\left(\frac{\mathrm{3}.\mathrm{3}}{\mathrm{2}}\right)=\mathrm{18} \\ $$
Commented by talminator2856791 last updated on 08/Sep/21
$$\:\mathrm{how}\:\mathrm{did}\:\mathrm{you}\:\mathrm{make}\:\mathrm{this}\:\mathrm{animation}?\: \\ $$