Lösungen/Solutions/
B1S1Ue/Ex12

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Remove["Global`*"]

Ueb/Ex 1      W

p1x = 2; p1y = 3; p2x = 10; p2y = 5;

Reduce[p4x - p2x == p2x - p3x, p3x]

fx[r_] := (p3x - p1x)/(p3x - 
                p2x) / ((p4x - p1x)/(p4x - p2x)) /. {p3x -> 
            20 - p4x}; fx[r]

Solve[fx[r] == -1, {r}]

Reduce[p4y - p2y == p2y - p3y, p3y]

fy[r_] := (p3y - p1y)/(p3y - 
                p2y) / ((p4y - p1y)/(p4y - 
                  p2y)) /. {p3y -> 10 - p4y}; fy[r]

Solve[fy[r] == -1, {r}]

Ueb/Ex 2      W

λ = -c/3  /(2/3 c)

μ = -a/2  /(a/2)

ν = -(1 - x) b /(x b)

Solve[λ μ ν  == -1, {x}]

Ueb/Ex 3      W

λ = -y/3  /(5 - y)

μ = -5/2  /(5/2)

ν = +10 /20

Solve[λ μ ν  == +1, {y}]

N[%]

Ueb/Ex 4      W

eq1 = ((y0 - 4)/4 == y0/(4 + x0));({{eq2 = ((y0 - 3)/4 == 
                    y0/(4 + x0 - a));   }, {eq3 = ((y0 - 1)/4 == y0/(4 + x0 - 2  a));}})

Solve[{eq1, eq2, eq3}, {x0, y0, a}]  // Flatten

% // N

v1 = ((2 - 3)/(2 - 1))/((4 - 3)/(4 - 
                1))

v2 = ((x1 - (16/3 - 7/3))/(x1 - (16/3 - 
                    2 7/3)))/
((16/
                  3 - (16/3 - 7/3))/(16/
                  3 - (16/3 - 2 7/3)))

Solve[v1 == v2, {x1}]

% // N

Ueb/Ex 5      W

Show[
        Graphics[{PointSize[0.03], 
Line[{{0, 5}, {8, 0}}], 
            Line[{{0, 0}, {8, 0}}], 
            Line[{{0, 5}, {0, 0}}], 
Point[{0, 
                0}], 
Line[{{0, 5}, {4, 0}}], 
            Line[{{0, 0}, {4, 2.5}}], 
            Line[{{8, 0}, {0, 2.5}}], 
Point[{8/3, 
                5/3}], 
Line[{{0, 2.5}, {4, 2.5}}], 
            Line[{{4, 0}, {4, 2.5}}], 
            Line[{{8/3, 5/3} + {2.5, 4}/3, {8/3, 
                    5/3} - {2.5, 4} 5/12}], 
Line[{{4, 
                    2.5} + {2.5, 4}/5, {4, 2.5} - {2.5, 4}/
                    2}], 
Point[{4, 
                2.5}]
}]];