优优班--学霸训练营 > 知识点挑题
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            • 1.

              直线\(2x-3y+2=0\)关于\(x\)轴对称的直线方程为\((\)     \()\)

              A.\(2x+3y+2=0\)
              B.\(2x+3y-2=0\)
              C.\(2x-3y-2=0\)
              D.\(2x-3y+2=0\) 
            • 2.

              已知直线\(l_{1}:mx-y+3=0\)与\(l_{2}\)关于直线\(y=x\)对称, \(l_{2}\)与\(l_{3}:y=-\dfrac{1}{2}x+\dfrac{1}{2}\)垂直,则\(m=\)  \((\)  \()\)

              A.\(-\dfrac{1}{2}\)
              B.\(\dfrac{1}{2}\)
              C.\(-2\)
              D.\(2\)
            • 3.
              点\(P(7,-4)\)关于直线\(l\):\(6x-5y-1=0\)的对称点\(Q\)的坐标是\((\)  \()\)
              A.\((5,6)\)
              B.\((2,3)\)
              C.\((-5,6)\)
              D.\((-2,3)\)
            • 4.

              在平面直角坐标系内,过定点\(P\)的直线\(l\):\(ax+y-1=0\)与过定点\(Q\)的直线\(m\):\(x-ay+3=0\)相交于点\(M\),则\(|MP|^{2}+|MQ|^{2}=(\)  \()\)


              A.\( \dfrac{ \sqrt{10}}{2}\)                
              B.\( \sqrt{10}\)

              C.\(5\)                                                           
              D.\(10\)
            • 5.

              下面给出四个命题的表述:

              \(①\)直线\((3+m)x+4y-3+3m=0(m∈R)\)恒过定点\((-3,3)\);

              \(②\)线段\(AB\)的端点\(B\)的坐标是\((3,4)\),\(A\)在圆\(x^{2}+y^{2}=4\)上运动,则线段\(AB\)的中点\(M\)的轨迹方程\({{\left( x-\dfrac{3}{2} \right)}^{2}}+{{(y-2)}^{2}}=1\);

              \(③\)已知\(M=\left\{ \left.\left(x,y\right) \right|y= \sqrt{1-{x}^{2}}\right\} \),\(N=\{(x,y)|y=x+b\}\),若\(M∩N\neq \varnothing \),则\(b∈\left[- \sqrt{2}, \sqrt{2}\right] \);

              \(④\)已知圆\(C:(x-b)^{2}+(y-c)^{2}=a^{2}(a > 0,b > 0,c > 0)\)与\(x\)轴相交,与\(y\)轴相离,则直线\(ax+by+c=0\)与直线\(x+y+1=0\)的交点在第二象限.

              其中表述正确的是  \((\)    \()\)

              A.\(①②④\)
              B.\(①②③\)
              C.\(①③\)
              D.\(①②③④\)
            • 6.

              若直线\(l\)\({\,\!}_{1}\):\(y\)\(=\)\(k\)\((\)\(x\)\(-4)\)与直线\(l\)\({\,\!}_{2}\)关于点\((2,1)\)对称,则直线\(l\)\({\,\!}_{2}\)恒过定点\((\)  \()\)

              A.\((0,4)\)                             
              B.\((0,2)\) 
              C.\((-2,4)\)                     
              D.\((4,-2)\)
            • 7. 在等腰直角三角形\(ABC\)中,\(AB=AC=4\),点\(P\)是边\(AB\)上异于\(A\),\(B\)的一点,光线从点\(P\)出发,经\(BC\),\(CA\)发射后又回到原点\(P(\)如图\().\)若光线\(QR\)经过\(\triangle ABC\)的重心,则\(BP\)等于(    )


              A.\(2\)      
              B.\(1\)      
              C.\( \dfrac{8}{3} \)      
              D.\( \dfrac{4}{3} \)
            • 8.

              \(\triangle ABC\)的三个顶点是\(A(0,3)\),\(B(3,3)\),\(C(2,0)\),直线\(l:x=a \)将\(\triangle ABC\)分割成面积相等的两部分,则\(a\)的值是                                                     

              A.\( \sqrt{3} \)
              B.\(1+ \dfrac{ \sqrt{2}}{2} \)
              C.\(1+ \dfrac{ \sqrt{3}}{3} \)
              D.\( \sqrt{2} \)
            • 9.
              平面直角坐标系中直线\(y=2x+1\)关于\(y=x-2\)对称的直线\(l\)方程为\((\)  \()\)
              A.\(x-4y-11=0\)
              B.\(4x-y+11=0\)
              C.\(x-2y+7=0\)
              D.\(x-2y-7=0\)
            • 10.
              入射光线沿直线\(x-2y+3=0\)射向直线\(l\):\(y=x\),被\(l\)反射后的光线所在直线的方程是\((\)  \()\)
              A.\(2x+y-3=0\)
              B.\(2x-y-3=0\)
              C.\(2x+y+3=0\)
              D.\(2x-y+3=0\)
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