Question

已知三点A（4,-2）,B（-4,4）,C（1,1）,过点C作向量CD与向量AB共线,且向量CD的模=5,则D点坐标为

Answer 1

设点D(x,y)

(y-1)/(x-1)=(-2-4)/(4+4)=-3/4

y=-3x/4+7/4

(x-1)²+(-3x/4+7/4-1)²=25

(x-1)²=16

x-1=±4

x=5 y=-2

或x=-3 y=4

所以点D为(5,-2)或(-3,4)