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2008-01-05 8:08 pm
若直線x+2y=0上的一點與原點的距離相等於該點與直線x+2y-3的距離,試求該點的坐標。

回答 (2)

2008-01-05 8:19 pm
✔ 最佳答案
設 (2t, -t ) 為該點的坐標

(2t)^2 + (-t)^2 = { [2t +2(-t) - 3 ] / sqrt(1^2 + 2^2) }^2
4t^2 + t^2 = [ -3 / sqrt(5) ]^2
5t^2 = 9/5
t = 3/5 or -3/5

故該點的坐標為 (6/5, -3/5) 或 (-6/5, 3/5)
2008-01-05 9:10 pm
let (2t, -t ) be the coordinate of this point

(2t)^2 + (-t)^2 = { [2t +2(-t) - 3 ] / sqrt(1^2 + 2^2) }^2
4t^2 + t^2 = [ -3 / sqrt(5) ]^2
5t^2 = 9/5
t = 3/5 or -3/5

so the coordinate of this point are (6/5, -3/5) or (-6/5, 3/5)


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