已知,如图,在平面直角坐标系内,点A的坐标为(0,24),经过原点的

已知,如图,在平面直角坐标系内,点A的坐标为(024),经过原点的直线l1与经过点A的直线l2相交于B,点B坐标为(186)

(1)求直线l1l2的表达式;

(2)C为线段OB上一动点(C不与点OB重合),作CDy轴交直线l2于点D,经过点CD分别向y轴作垂线,垂足分别为FE,得到矩形CDEF.

设点C的纵坐标为a,求点D的坐标(用含a的代数式表示)

若矩形CDEF的面积为60,请直接写出此时点C的坐标.     

答案

解:(1)设直线l1的表达式为yk1x,它过B(186)

18k16k1(2)∴yx.(3)

设直线l2的表达式为yk2xb,它过A(024)B(186),得

y=-x24.(6)

(2)①∵C在直线l1上,且点C的纵坐标为aaxx3a

C的坐标为(3aa)∵CDy轴,D的横坐标为3a.

D在直线l2上,y=-3a24D(3a,-3a24)(10)

C(31)C(155)(12)

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