首先畫L嘅graph
Construct幾條OP嘅possible line 跟住mark得幾個Q嘅position 其實已經肯定Q嘅Locus係parallel to L
當然呢個係直觀嘅諗法 如果解釋嘅 咪試下搵L同兩軸嘅交點 跟住搵呢兩點分別同O嘅mid-point 再計slope
不過唔係最嚴謹嘅做法嚟 因為咁做其實assume Q嘅locus係直線 但我哋冇prove 但我覺得core做到咁都接受㗎啦
如果真係要嚴謹嘅證明可以咁做
Let (m, n) be the coordinates of P.
So, we have 3m + n - 1 = 0 ……… (*)
Let (x, y) be the coordinates of Q.
Note that x = (m + 0)/2 and y = (n + 0)/2.
So, we have m = 2x and n = 2y.
Substituting into (*), we have 6x + 2y - 1 = 0.
Thus, the equation of the locus of Q is 6x + 2y - 1 = 0