1、左图。S△ABC(黑线 ) =S□AFED - ( S△ACF +S△BCE +S△ABD )= 5 * 4 - ( 4 * 2 + 3 * 2 + 5 * 2 )/2= 20 - 12= 82、㈠ AC平分□AFCQ,由1,已知S△ACF = 4,S△ACQ = 4,故Q ( 1,2 );㈡ Q为直线 y = x + 1在一象限上任意一点;① 当x < 1时(图中粉线 );S△ACQ =S△APQ +S△APC= AP( 1 - x )/2 + AP * ( 5 - 1 )/2=AP( 1 - x + 4 )/2= AP( 5 - x )/2;直线CQ y =ax + b,在点C, 5a + b = 2,b = 2 - 5a,y = ax - 5a + 2;在点Q,ax - 5a + 2 = x + 1,a( x - 5 ) = x - 1,a = ( x - 1 )/( x - 5 );a表达式中的x是点Q的x值;在点P,x1 = 1,AP = y =( x - 1 )/( x - 5 ) - 5( x - 1 )/( x - 5 ) + 2( x - 5 )/( x - 5 )= 2( x + 3 )/( 5 - x )S△ACQ = 2( x + 3 )/( 5 -x) * ( 5 - x )/2=x + 3;② 当 x > 1 时( 图中蓝线 );S△ACQ = S△PCQ + S△APC= CP( x + 1 - 2 )/2 + CP * 2/2= CP( x + 1 )/2;直线AQ y = ax + b;在点A,a+ b = 0,b = -a,y = ax - a = a( x - 1 );在点Q,a( x - 1 ) = x + 1,a = ( x + 1 )/( x - 1 );a 表达式中的 x 是 点Q 的 x 值;在点P,y = 2,x1 - 1 = 2/a,x1 = 2( x - 1 )/( x + 1 ) + 1 = ( 3x - 1 )/( x + 1 );CP = 5 -x1 = 5( x + 1 )/( x + 1 ) -( 3x - 1 )/( x + 1 ) = 2( x + 3 )/( x + 1 );S△ACQ = 2( x + 3 )/( x + 1 ) * ( x + 1 )/2= x + 3;故△ACQ面积S 与点Qx值的函数关系是S =x + 3 。3、右图作点C关于 x轴的对称点C‘,BC’交 x 轴于P;BP + PC =BP +PC‘ =BC‘,B、C’之间直线最短,所以BP + PC有最小值;BP + PC = BC‘ =√( 7^2 + 2^2 ) =√53;直线BC’ y = ax + b;在点B,3a + b = 5;在点C‘,5a + b = -2;解方程组,a = - 7/2,b = 31/2,y = -7x/2 + 31/2;点P-7x/2 + 31/2 = 0,x = 31/7;点P坐标 ( 31/7,0 ) 。