在直角坐标系中，O是坐标原点，P1（x1，y1）、P2（x2，y2）是第一象限的两个点，若1，x1，x2，4依次成等差数列，而1，y1，y2，8依次成等比数列，则△OP1P2的面积是______．
因为P1（x1，y1）、P2（x2，y2）是第一象限的两个点，所以x1，x2，y1，y2均为正数，
由1，x1，x2，4依次成等差数列，设其公差为d，则4=1+3d，所以d=1，所以，x1=2，x2=3．
由1，y1，y2，8依次成等比数列，设其公比为q，则8=1×q3，所以q=2，所以y1=2，y2=4
所以P1（2，2），P2（3，4），
所以|OP1|=
=222+22
，|OP2|=2
=532+42
|P1P2|=
=(3-2)2+(4-2)2
，5
所以cos∠P1OP2=
=(2
)2+52-2
25 2×2
×52 7 2 10
所以sin∠P1OP2=
，2 10
所以S△P1OP2=
×21 2
×5×2
=1．2 10
故答案为1．
故选A．
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