平行四邊形的面積
Author: 藍邦偉  老師

行列式與面積

四邊形ABCD的面積是

A = (0, 0)
B = (-0.64, 4.48)
D = (4.3, 1.12)
u = Vector(A, B)
v = Vector(A, D)
C: B + D - A
a = Segment(D, C)
b = Segment(C, B)
a_{11}: x(B) - x(A)
a_{21}: y(B) - y(A)
a_{12}: x(D) - x(A)
a_{22}: y(D) - y(A)
文字5: "|\left|\begin{array}{cc} " + a_{11} + " &" + a_{12} + " \\" + a_{21} + " &" + a_{22} + " \\ \end{array}\right||"
文字6: "=|" + (If[a_{11} * a_{22} > 0, "", "-"]) + (abs(a_{11})) + "\times{}" + (abs(a_{22})) + (If[a_{12} * a_{21} < 0, "+", "-"]) + (abs(a_{12})) + "\times{}" + (abs(a_{21})) + "|"
文字7: "=" + (LaTeX[Area[A, B, C, D]]) + ""
文字2: "\vec{ u }= \left[\begin{array}{cc} " + (LaTeX[x(B) - x(A)]) + "  \\ " + (LaTeX[y(B) - y(A)]) + "\\ \end{array}\right]=(" + (LaTeX[x(B) - x(A)]) + "," + (LaTeX[y(B) - y(A)]) + ")"
文字3: "\vec{ v } =\left[\begin{array}{cc} " + (LaTeX[x(D) - x(A)]) + " \\" + (LaTeX[y(D) - y(A)]) + " \\ \end{array}\right]=(" + (LaTeX[x(D) - x(A)]) + "," + (LaTeX[y(D) - y(A)]) + ")"
text1: "$=| \left\vert  \begin{array}{cc} " + (LaTeX[x(B) - x(A)]) + " & " + (LaTeX[y(B) - y(A)]) + " \\ " + (LaTeX[x(D) - x(A)]) + " & " + (LaTeX[y(D) - y(A)]) + " \\ \end{array} \right\vert | $"