Question

5．已知點(diǎn)A（2a+3b，-2）與點(diǎn)B（-8，3a+2b）關(guān)于坐標(biāo)原點(diǎn)對(duì)稱，則a+b=2．

Answer 1

分析 直接利用關(guān)于原點(diǎn)對(duì)稱點(diǎn)的性質(zhì)得出關(guān)于a，b的等式進(jìn)而求出答案．

解答 解：∵點(diǎn)A（2a+3b，-2）與點(diǎn)B（-8，3a+2b）關(guān)于坐標(biāo)原點(diǎn)對(duì)稱，
∴$\left\{\begin{array}{l}{2a+3b=8}\\{3a+2b=2}\end{array}\right.$，
故5a+5b=10，
則a+b=2．
故答案為：2．

點(diǎn)評(píng) 此題主要考查了關(guān)于原點(diǎn)對(duì)稱點(diǎn)的性質(zhì)，正確記憶橫縱坐標(biāo)的關(guān)系是解題關(guān)鍵．