Question

OABC是一张放在平面直角坐标系内中的长方形纸片,O为原点,点A在X轴的正半轴上,点C在Y轴的正半轴上,OA=10

Answer 1

A(10,0),C(0,8),B(10,8)

设D(0,d),E(e,8),8 > d > 0,10 > e > 0

AD为OE的垂直平分线

OE的斜率k = 8/e

AD的斜率k' = -1/k = -e/8 = (d - 0)/(0 - 10) = -d/10

e = 4d/5 (1)

AD的方程:x/10 + y/d = 1

OE的中点为M(e/2,4),M在AD上:

e/20 + 4/d = 1 (2)

由(1)(2)得:d² - 25d + 100 = (d - 5)(d - 20) = 0

d = 5 (舍去d = 20 > 8),D(0,5)

e = 4,E(4,8)