3.3.2 两点间的距离
课后篇巩固探究
1.已知点A(-2,-1),B(a,3),且|AB|=5,则a的值为0( )
A.1 B.-5
C.1或-5 D.-1或5
解析由|AB|=√("(" a+2")" ^2+"(" 3+1")" ^2 )=5,得(a+2)2=9,解得a=1或-5.
答案C
2.已知△ABC的顶点A(2,3),B(-1,0),C(2,0),则△ABC的周长是( )
A.2√3 B.3+2√3
C.6+3√2 D.6+√10
解析∵|AB|=√("(-" 1"-" 2")" ^2+"(" 0"-" 3")" ^2 )=3√2,|BC|=3,|AC|=√("(" 2"-" 2")" ^2+"(" 0"-" 3")" ^2 )=3,
∴△ABC的周长为6+3√2.
答案C
3.已知点A(x,5)关于点(1,y)的对称点为(-2,-3),则点P(x,y)到原点的距离是( )
A.2 B.4 C.5 D.√17
解析根据中点坐标公式,得(x"-" 2)/2=1,且(5"-" 3)/2=y.
解得x=4,y=1,所以点P的坐标为(4,1),则点P(x,y)到原点的距离d=√("(" 4"-" 0")" ^2+"(" 1"-" 0")" ^2 )=√17.
答案D
4.到点A(1,3),B(-5,1)的距离相等的动点P满足的方程是( )
A.3x-y-8=0
B.3x+y+4=0
C.3x-y+6=0
D.3x+y+2=0
解析设P(x,y),则√("(" x"-" 1")" ^2+"(" y"-" 3")" ^2 )=√("(" x+5")" ^2+"(" y"-" 1")" ^2 ),即3x+y+4=0.
答案B
5.若点P(x,y)在直线4x+3y=0上,且x,y满足-14≤x-y≤7,则点P到坐标原点距离的取值范围是( )
A.[0,5] B.[0,10]
C.[5,10] D.[5,15]
解析∵点P(x,y)在直线4x+3y=0上,且x,y满足-14≤x-y≤7,∴-6≤x≤3.
∵线段4x+3y=0(-6≤x≤3)过原点,