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数学
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如图,双曲线
y=
k
x
经过点A(2,2)与点B(4,m),求△AOB的面积.
人气:302 ℃ 时间:2020-02-04 01:49:59
解答
过A、B分别作x轴的垂线,垂足分别为C、D,如图,
∵双曲线y=
k
x
经过点A(2,2),
∴k=2×2=4,
而点B(4,m)在y=
4
x
上,
∴4•m=4,
解得m=1,
即B点坐标为(4,1)
∴S
△AOB
=S
△AOC
+S
梯形ABDC
-S
△BOD
,
=
1
2
OC•AC+
1
2
×(AC+BD)×CD-
1
2
×OD×BD,
=
1
2
×2×2+
1
2
×(2+1)×(4-2)-
1
2
×4×1,
=3.
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