在平面直角坐標(biāo)系中,對于任意兩點(diǎn)A(x1,y1)和B(x2,y2),稱點(diǎn)(x1x2,y1y2)為點(diǎn)A和B的融合點(diǎn).如(2,3)和(1,4)的融合點(diǎn)是(2,12).
(1)點(diǎn)(3,2)和(0.5,6)的融合點(diǎn)坐標(biāo)是 (1.5,12)(1.5,12);
(2)已知點(diǎn)P(3,1)和直線l:y=-2x+4.設(shè)點(diǎn)Q是直線l上任意一點(diǎn),點(diǎn)P和Q的融合點(diǎn)為點(diǎn)T.
①求證:當(dāng)點(diǎn)Q在直線l上移動時(shí),點(diǎn)T始終在同一條直線上.
②若M(-1,0),N(0,-23),求△MNT的面積.
(2)對于點(diǎn)C(m,n)(mn≠0)和直線h:y=kx+b(k≠0),點(diǎn)D是直線h上任意一點(diǎn),類似(2),可證明當(dāng)點(diǎn)D在直線h上移動時(shí),點(diǎn)C和D的融合點(diǎn)始終在同一條直線上,稱該直線為點(diǎn)C和直線h的融合直線.已知直線s:y=3x+4,點(diǎn)R在直線x=2上且縱坐標(biāo)不為0,點(diǎn)R和直線s的融合直線記為t.點(diǎn)E(-2,2)點(diǎn)F(2,-2),若融合直線t與線段EF有公共點(diǎn),請直接寫出點(diǎn)R的縱坐標(biāo)yR的取值范圍.
M
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1
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0
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N
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0
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2
3
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【考點(diǎn)】一次函數(shù)圖象上點(diǎn)的坐標(biāo)特征;一次函數(shù)的性質(zhì).
【答案】(1.5,12)
【解答】
【點(diǎn)評】
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發(fā)布:2024/5/29 8:0:9組卷:254引用:1難度:0.3
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