新高考數(shù)學(xué)一輪復(fù)習(xí)講義 第38講 兩條直線的位置關(guān)系（原卷版）

第38講兩條直線的位置關(guān)系（精講）題型目錄一覽①兩條直線的位置關(guān)系②兩條直線的交點(diǎn)和距離問題③對稱問題Ⅰ-點(diǎn)關(guān)于點(diǎn)和線關(guān)于點(diǎn)④對稱問題Ⅱ-點(diǎn)關(guān)于線和線關(guān)于線⑤直線的綜合問題一、知識點(diǎn)梳理一、知識點(diǎn)梳理一、兩直線平行與垂直的判定兩條直線平行與垂直的判定以表格形式出現(xiàn)，如表所示．兩直線方程平行垂直SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0（斜率存在）SKIPIF1<0（斜率不存在）SKIPIF1<0或SKIPIF1<0SKIPIF1<0或SKIPIF1<0中有一個(gè)為0，另一個(gè)不存在．二、三種距離1．兩點(diǎn)間的距離平面上兩點(diǎn)SKIPIF1<0的距離公式為SKIPIF1<0．特別地，原點(diǎn)O（0，0）與任一點(diǎn)P（x，y）的距離SKIPIF1<02．點(diǎn)到直線的距離點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離SKIPIF1<0特別地，若直線為l：x=m，則點(diǎn)SKIPIF1<0到l的距離SKIPIF1<0；若直線為l：y=n，則點(diǎn)SKIPIF1<0到l的距離SKIPIF1<03．兩條平行線間的距離已知SKIPIF1<0是兩條平行線，求SKIPIF1<0間距離的方法：（1）轉(zhuǎn)化為其中一條直線上的特殊點(diǎn)到另一條直線的距離．（2）設(shè)SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0之間的距離SKIPIF1<0注：兩平行直線方程中，x，y前面對應(yīng)系數(shù)要相等．4．雙根式雙根式SKIPIF1<0型函數(shù)求解，首先想到兩點(diǎn)間的距離，或者利用單調(diào)性求解．三、直線中的對稱問題1．點(diǎn)關(guān)于點(diǎn)對稱點(diǎn)關(guān)于點(diǎn)對稱的本質(zhì)是中點(diǎn)坐標(biāo)公式：設(shè)點(diǎn)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0，則根據(jù)中點(diǎn)坐標(biāo)公式，有SKIPIF1<0，可得對稱點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<02．點(diǎn)關(guān)于直線對稱點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0對稱的點(diǎn)為SKIPIF1<0，連接SKIPIF1<0，交SKIPIF1<0于SKIPIF1<0點(diǎn)，則SKIPIF1<0垂直平分SKIPIF1<0，所以SKIPIF1<0，且SKIPIF1<0為SKIPIF1<0中點(diǎn)，又因?yàn)镾KIPIF1<0在直線SKIPIF1<0上，故可得SKIPIF1<0，解出SKIPIF1<0即可．3．直線關(guān)于點(diǎn)對稱法一：在已知直線上取兩點(diǎn)，利用中點(diǎn)坐標(biāo)公式求出它們關(guān)于已知點(diǎn)對稱的兩點(diǎn)坐標(biāo)，再由兩點(diǎn)式求出直線方程；法二：求出一個(gè)對稱點(diǎn)，再利用兩對稱直線平行，由點(diǎn)斜式得到所求直線方程．4．直線關(guān)于直線對稱求直線SKIPIF1<0，關(guān)于直線SKIPIF1<0（兩直線不平行）的對稱直線SKIPIF1<0第一步：聯(lián)立SKIPIF1<0算出交點(diǎn)SKIPIF1<0第二步：在SKIPIF1<0上任找一點(diǎn)（非交點(diǎn)）SKIPIF1<0，利用點(diǎn)關(guān)于直線對稱的秒殺公式算出對稱點(diǎn)SKIPIF1<0第三步：利用兩點(diǎn)式寫出SKIPIF1<0方程5．常見的一些特殊的對稱點(diǎn)SKIPIF1<0關(guān)于SKIPIF1<0軸的對稱點(diǎn)為SKIPIF1<0，關(guān)于SKIPIF1<0軸的對稱點(diǎn)為SKIPIF1<0．點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0，關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0．點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0，關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0．點(diǎn)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0．點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0，關(guān)于直線SKIPIF1<0的對稱點(diǎn)為SKIPIF1<0．四、直線系方程1．過定點(diǎn)直線系過已知點(diǎn)SKIPIF1<0的直線系方程SKIPIF1<0（SKIPIF1<0為參數(shù)）．2．斜率為定值直線系斜率為SKIPIF1<0的直線系方程SKIPIF1<0（SKIPIF1<0是參數(shù)）．3．平行直線系與已知直線SKIPIF1<0平行的直線系方程SKIPIF1<0（SKIPIF1<0為參數(shù)）．4．垂直直線系與已知直線SKIPIF1<0垂直的直線系方程SKIPIF1<0（SKIPIF1<0為參數(shù)）．5．過兩直線交點(diǎn)的直線系過直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)的直線系方程：SKIPIF1<0（SKIPIF1<0為參數(shù)）．二、題型分類精講二、題型分類精講題型一兩條直線的位置關(guān)系策略方法由一般式確定兩直線位置關(guān)系的方法判斷兩直線的位置關(guān)系可以從斜率是否存在分類判斷，也可以按照以下方法判斷：一般地，設(shè)SKIPIF1<0（SKIPIF1<0不全為0），SKIPIF1<0（SKIPIF1<0不全為0），則：當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0相交；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0直線平行或重合，代回檢驗(yàn)；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0直線垂直，與向量的平行與垂直類比記憶．【典例1】（單選題）若直線SKIPIF1<0：SKIPIF1<0?與直線SKIPIF1<0：SKIPIF1<0平行，則SKIPIF1<0?的值為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0? C．SKIPIF1<0?或SKIPIF1<0 D．SKIPIF1<0【典例2】（單選題）直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，則“SKIPIF1<0或SKIPIF1<0”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分又不必要條件【題型訓(xùn)練】一、單選題1．直線SKIPIF1<0與SKIPIF1<0平行，則實(shí)數(shù)SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．02．直線SKIPIF1<0過點(diǎn)SKIPIF1<0且與直線SKIPIF1<0垂直，則SKIPIF1<0的方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．若平面內(nèi)兩條平行線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0間的距離為SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0（

）A．2 B．－2或1 C．－1 D．－1或24．已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件5．知直線SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．26．已知直線SKIPIF1<0與直線SKIPIF1<0垂直，若直線SKIPIF1<0的傾斜角為SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0，則“直線SKIPIF1<0與直線SKIPIF1<0垂直”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件，二、多選題8．已知直線SKIPIF1<0，其中SKIPIF1<0，則（

）A．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0與直線SKIPIF1<0垂直B．若直線SKIPIF1<0與直線SKIPIF1<0平行，則SKIPIF1<0C．直線SKIPIF1<0過定點(diǎn)SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，直線SKIPIF1<0在兩坐標(biāo)軸上的截距相等9．已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0（SKIPIF1<0），則（

）A．直線SKIPIF1<0過定點(diǎn)SKIPIF1<0 B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 D．當(dāng)SKIPIF1<0時(shí)，兩直線SKIPIF1<0，SKIPIF1<0之間的距離為3三、填空題10．已知點(diǎn)SKIPIF1<0，直線SKIPIF1<0，則過點(diǎn)P且與直線l相交的一條直線的方程是．11．若直線SKIPIF1<0與SKIPIF1<0垂直，則SKIPIF1<0.12．已知兩條平行直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0間的距離為.13．已知經(jīng)過點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0的直線l1與經(jīng)過點(diǎn)SKIPIF1<0和點(diǎn)SKIPIF1<0的直線SKIPIF1<0互相垂直，則實(shí)數(shù)SKIPIF1<0.14．在SKIPIF1<0中，SKIPIF1<0的內(nèi)角平分線方程為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則角SKIPIF1<0的正切值為．題型二兩條直線的交點(diǎn)和距離問題策略方法1．求過兩直線交點(diǎn)的直線方程的方法求過兩直線交點(diǎn)的直線方程，先解方程組求出兩直線的交點(diǎn)坐標(biāo)，再結(jié)合其他條件寫出直線方程，也可借助直線系方程，利用待定系數(shù)法求出直線方程，這樣能簡化解題過程．2．點(diǎn)到直線、兩平行線間的距離公式的使用條件(1)求點(diǎn)到直線的距離時(shí)，應(yīng)先化直線方程為一般式．(2)求兩平行線之間的距離時(shí)，應(yīng)先將方程化為一般式且x，y的系數(shù)對應(yīng)相等．【典例1】（單選題）若直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)在第一象限，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】（單選題）設(shè)直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)為P，則P到直線SKIPIF1<0的距離為（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．坐標(biāo)原點(diǎn)O到直線l：SKIPIF1<0的距離是（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<02．若直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)在直線SKIPIF1<0上，則實(shí)數(shù)SKIPIF1<0（

）A．4 B．2 C．SKIPIF1<0 D．SKIPIF1<03．已知直線SKIPIF1<0，SKIPIF1<0，給出命題SKIPIF1<0：直線SKIPIF1<0和SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)關(guān)于SKIPIF1<0軸對稱，SKIPIF1<0：直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)在直線SKIPIF1<0上．則（

）A．SKIPIF1<0假SKIPIF1<0真 B．SKIPIF1<0真SKIPIF1<0真 C．SKIPIF1<0假SKIPIF1<0假 D．SKIPIF1<0真SKIPIF1<0假4．設(shè)SKIPIF1<0為動點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．35．若點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為d，則d的最大值為（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．SKIPIF1<06．已知實(shí)數(shù)SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知兩條直線SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，當(dāng)兩平行線距離最大時(shí)，SKIPIF1<0（

）A．3 B．4 C．5 D．68．若直線SKIPIF1<0與直線SKIPIF1<0的交點(diǎn)位于第一象限，則直線l的傾斜角的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知直線SKIPIF1<0，點(diǎn)SKIPIF1<0，記SKIPIF1<0到SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題10．已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0（SKIPIF1<0），則（

）A．直線SKIPIF1<0過定點(diǎn)SKIPIF1<0 B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0 D．當(dāng)SKIPIF1<0時(shí)，兩直線SKIPIF1<0，SKIPIF1<0之間的距離為311．設(shè)直線系SKIPIF1<0，下列命題中的真命題有（

）A．SKIPIF1<0中所有直線均經(jīng)過一個(gè)定點(diǎn)B．存在定點(diǎn)SKIPIF1<0不在SKIPIF1<0中的任一條直線上C．對于任意整數(shù)SKIPIF1<0，存在正SKIPIF1<0邊形，其所有邊均在SKIPIF1<0中的直線上D．SKIPIF1<0中的直線所能圍成的正三角形面積都相等12．函數(shù)SKIPIF1<0圖象上一點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題13．經(jīng)過兩條直線SKIPIF1<0，SKIPIF1<0的交點(diǎn)，且直線的一個(gè)方向向量SKIPIF1<0的直線方程為．14．已知兩條平行直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，則SKIPIF1<0與SKIPIF1<0間的距離為.15．已知直線SKIPIF1<0：SKIPIF1<0，過點(diǎn)SKIPIF1<0作直線SKIPIF1<0，則SKIPIF1<0和SKIPIF1<0的交點(diǎn)坐標(biāo)為．（用含A，B的式子表示）16．若SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0在線段SKIPIF1<0（含端點(diǎn)）上移動，則SKIPIF1<0的最小值為.17．在SKIPIF1<0中，SKIPIF1<0的內(nèi)角平分線方程為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則角SKIPIF1<0的正切值為．18．SKIPIF1<0的三個(gè)頂點(diǎn)到直線SKIPIF1<0的距離分別為1，2，3，則該三角形的重心SKIPIF1<0到直線SKIPIF1<0的距離為（答案不唯一，填一個(gè)即可）．題型三對稱問題Ⅰ-點(diǎn)關(guān)于點(diǎn)和線關(guān)于點(diǎn)策略方法對稱問題的求解方法(1)點(diǎn)關(guān)于點(diǎn)：點(diǎn)P(x，y)關(guān)于點(diǎn)Q(a，b)的對稱點(diǎn)P′(x′，y′)滿足eq\b\lc\{\rc\(\a\vs4\al\co1(x′＝2a－x，,y′＝2b－y.))(2)線關(guān)于點(diǎn)：直線關(guān)于點(diǎn)的對稱可轉(zhuǎn)化為點(diǎn)關(guān)于點(diǎn)的對稱問題來解決．【典例1】（單選題）已知不同的兩點(diǎn)SKIPIF1<0與SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對稱，則SKIPIF1<0（

）A．SKIPIF1<0 B．14 C．SKIPIF1<0 D．5【典例2】（單選題）不論實(shí)數(shù)SKIPIF1<0取何值時(shí)，直線SKIPIF1<0都過定點(diǎn)SKIPIF1<0，則直線SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對稱直線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，直線SKIPIF1<0與SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對稱，則一定在直線SKIPIF1<0上的點(diǎn)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．將一張坐標(biāo)紙折疊一次，使點(diǎn)SKIPIF1<0與SKIPIF1<0重合，求折痕所在直線是（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知直線SKIPIF1<0與SKIPIF1<0關(guān)于原點(diǎn)對稱，若SKIPIF1<0的方程是SKIPIF1<0，則SKIPIF1<0的方程是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．直線ax＋y＋3a－1＝0恒過定點(diǎn)M，則直線2x＋3y－6＝0關(guān)于點(diǎn)M對稱的直線方程為（

）A．2x＋3y－12＝0 B．2x＋3y＋12＝0 C．3x－2y－6＝0 D．2x＋3y＋6＝05．直線SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對稱的直線方程為（

）A．4x＋3y－4＝0 B．4x＋3y－12＝0C．4x－3y－4＝0 D．4x－3y－12＝06．已知點(diǎn)SKIPIF1<0且線段SKIPIF1<0的垂直平分線的方程是SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．17．在SKIPIF1<0中，已知點(diǎn)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0邊的中點(diǎn)M在SKIPIF1<0軸上，SKIPIF1<0邊的中點(diǎn)N在SKIPIF1<0軸上，則直線SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型四對稱問題Ⅱ-點(diǎn)關(guān)于線和線關(guān)于線策略方法對稱問題的求解方法(1)點(diǎn)關(guān)于線：點(diǎn)A(a，b)關(guān)于直線Ax＋By＋C＝0(B≠0)的對稱點(diǎn)A′(m，n)，則有eq\b\lc\{\rc\(\a\vs4\al\co1(\f(n－b,m－a)×\b\lc\(\rc\)(\a\vs4\al\co1(－\f(A,B)))＝－1，,A·\f(a＋m,2)＋B·\f(b＋n,2)＋C＝0.))(2)線關(guān)于線：直線關(guān)于直線的對稱可轉(zhuǎn)化為點(diǎn)關(guān)于直線的對稱問題來解決．【典例1】（單選題）已知點(diǎn)A（a+2，b+2）和B（b-a，-b）關(guān)于直線4x+3y=11對稱，則a，b的值為（）.A．a(chǎn)=-1，b=2 B．a(chǎn)=4，b=-2C．a(chǎn)=2，b=4 D．a(chǎn)=4，b=2【典例2】（單選題）已知一條光線從點(diǎn)SKIPIF1<0射出，經(jīng)直線SKIPIF1<0反射后經(jīng)過點(diǎn)SKIPIF1<0，則反射光線所在直線的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．唐代詩人李頎的詩《古從軍行》開頭兩句說：“白日登山望烽火，黃昏飲馬傍交河．”詩中隱含著一個(gè)有趣的數(shù)學(xué)問題——“將軍飲馬”問題，即將軍在觀望烽火之后從山腳下某處出發(fā)，先到河邊飲馬后再回到軍營，怎樣走才能使總路程最短？在平面直角坐標(biāo)系中，設(shè)軍營所在位置為SKIPIF1<0，若將軍從點(diǎn)SKIPIF1<0處出發(fā)，河岸線所在直線方程為SKIPIF1<0，則“將軍飲馬”的最短總路程為（

）A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．SKIPIF1<02．一條光線從點(diǎn)SKIPIF1<0射出，傾斜角為SKIPIF1<0，遇SKIPIF1<0軸后反射，則反射光線的直線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知點(diǎn)P在直線SKIPIF1<0上,SKIPIF1<0,則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，一束光線從點(diǎn)SKIPIF1<0出發(fā)經(jīng)AC反射后，再經(jīng)BC上點(diǎn)D反射，落到點(diǎn)SKIPIF1<0上．則點(diǎn)D的坐標(biāo)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題6．點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)的坐標(biāo)是．7．如圖已知SKIPIF1<0，若光線SKIPIF1<0從點(diǎn)SKIPIF1<0射出，直線SKIPIF1<0反射后到直線SKIPIF1<0上，在經(jīng)直線SKIPIF1<0反射回原點(diǎn)SKIPIF1<0，則光線SKIPIF1<0所在的直線方程為．8．已知SKIPIF1<0的頂點(diǎn)SKIPIF1<0，SKIPIF1<0，一條角平分線所在直線為SKIPIF1<0，則點(diǎn)A坐標(biāo)為.9．在等腰直角三角形ABC中，SKIPIF1<0，點(diǎn)P是邊AB上異于A，B的一點(diǎn)，光從點(diǎn)P出發(fā)經(jīng)SKIPIF1<0反射后又回到點(diǎn)P，反射點(diǎn)為Q，R，若光線QR經(jīng)過SKIPIF1<0的重心，則SKIPIF1<0.10．以SKIPIF1<0為一個(gè)頂點(diǎn)，試在x軸上找一點(diǎn)B，直線l：SKIPIF1<0上找一點(diǎn)C，構(gòu)成SKIPIF1<0，則SKIPIF1<0的最小周長為.題型五直線的綜合問題策略方法處理直線方程綜合應(yīng)用的兩大策略(1)求解與直線方程有關(guān)的最值問題，先求出斜率或設(shè)出直線方程，建立目標(biāo)函數(shù)，再利用基本不等式求解最值．(2)含有參數(shù)的直線方程可看作直線系方程，這時(shí)要能夠整理成過定點(diǎn)的直線系，即能夠看出“動中有定”．【典例1】（單選題）過定點(diǎn)A的直線SKIPIF1<0與過定點(diǎn)SKIPIF1<0的直線SKIPIF1<0交于點(diǎn)SKIPIF1<0與SKIPIF1<0不重合），則SKIPIF1<0面積的最大值為（

）