在平行四边形ABCD中,A(1,1),向量AB=(6,0),点M是线段AB的中点,线段CM与BD交于点P.

1个回答

  • (1)若向量AD=(3,5),求点C的坐标;

    BC=AD=(3,5).A(1,1),向量AB=(6,0),∴B(7,1).C(10,6).

    (2)设P(x,y),当AB向量的模等于AD 向量的模时,求x,y满足的关系式.

    |AD|=6,设AB=a, AD=b.

    AP=a/2+t(a/2+b)=a+s(b-a).得到s=t=1/3.

    设D(u,v)(u-1)²+(v-1)²=36,P(x,y)

    (x-1,y-1)=AP=2a/3+b/3=(u/3+11/3,v/3-1/3)

    x=u/3+14/3,y=v/3+2/3. (u-1)²+(v-1)²=36

    x,y满足的关系式:(3x-14)²+(3y-3)²=36