已知直角坐标系中,点A(6,0),点B(0,8),点C(-4,0),点M从C出发,沿着CA方向,以每秒2个单位的速度向点
2个回答

(1) CM=2t AM=6-(-4)-2t=10-2t

M坐标(-4+2t,0)

AN=5t

N坐标(6-3t,4t)

MN=根号[(6-3t+4-2t)^2+(4t)^2]=根号(100-100t+41t^2)

MN⊥AB

=>MN^2+AN^2=AM^2

=>(100-100t+41t^2)+(5t)^2=(10-2t)^2

=>t=30/31

(2) MP:PN=M点横坐标的绝对值:N点横坐标的绝对值=|2t-4|:|6-3t|=(4-2t)/(6-3t)=2/3 (t