數線上的分點公式(2)
Author: 藍邦偉老師

$ 數線上的分點公式 $
$(2)\;如何以內分點公式求外分點$

$ P(x) $

$P(x)$

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
A_1 = (-3.3566577540000053, 0.05902581400000559)
B_1 = (6.3869277460000005, 0.1369744980000055)
A = DynamicCoordinates(A_1, floor(x(A_1)), 0)
B = DynamicCoordinates(B_1, floor(x(B_1)), 0)
m = 1 (slider from 1 to 5, step 1)
n = 2 (slider from 1 to 5, step 1)
t_B: "$ B(" + (LaTeX[x(B)]) + ") $"
t_A: "$A( " + (LaTeX[x(A)]) + " )$"
a: x(A)
b: x(B)
text2: "$\;\;\;\;\; " + (LaTeX[b]) + " =\frac{" + (LaTeX[n]) + "" + (LaTeX[If[a ≥ 0, "×" * a, If[a < 0, "×(" * a * ")"]]]) + "+" + (LaTeX[If[m - n ≠ 1, m - n, ""]]) + "x}{" + (LaTeX[m]) + "}$
$⇒" + (LaTeX[m * b]) + "=" + (LaTeX[a * n]) + "+" + (LaTeX[If[m - n ≠ 1, m - n, ""]]) + "x$
$⇒x=\frac{" + (LaTeX[m * b - n * a]) + "}{" + (LaTeX[m - n]) + "}=" + (LaTeX[FractionText[(m * b - n * a) / (m - n)]]) + "$"
P_1: ((m * b - n * a) / (m - n), 0)
P_2: ((-m * b + n * a) / (n - m), 0)
text3: "$\;\;\; " + (LaTeX[a]) + "=\frac{" + (LaTeX[m]) + "" + (LaTeX[If[b ≥ 0, "×" * b, "×(" * b * ")"]]) + "+" + (LaTeX[If[n - m ≠ 1, n - m, ""]]) + "x}{" + (LaTeX[n]) + "} $
$⇒" + (LaTeX[n * a]) + "=" + (LaTeX[m * b]) + "+" + (LaTeX[If[n - m ≠ 1, n - m, ""] * m]) + "x$
$⇒x=\frac{" + (LaTeX[n * a - b * m]) + "}{" + (LaTeX[n - m]) + "}=" + (LaTeX[FractionText[(n * a - m * b) / (n - m)]]) + "$"
C = (-15.711524168000013, 8.009791581999997)
text1: "$已知數線上兩點A(" + (LaTeX[x(A)]) + ")與B(" + (LaTeX[x(B)]) + ")，\;\frac{\overline{PA}}{\overline{PB}}=\frac{" + (LaTeX[m]) + "}{" + (LaTeX[n]) + "}，且\;P\;在\overline{AB}外，\;試求\;P\;點座標. $"