Vrcholy štvorca - súradnice

Mám vrcholy štvorca A / -3; 1/a B/1; 4 /. Urči súradnice vrcholov C a D, C 'a D'. Vďaka Petr.

Správna odpoveď:

x₂ = 2,9696
y₂ = -0,5957
x₃ = -1,0304
y₃ = -3,5957
x₄ = -0,9696
y₄ = 8,5957
x₅ = -4,9696
y₅ = 5,5957

x_{0} = - 3 y_{0} = 1 x_{1} = 1 y_{1} = 4 a = (x_{0} - x_{1})^{2} + (y_{0} - y_{1})^{2} = ((- 3) - 1)^{2} + (1 - 4)^{2} = 5 t g α = \frac{y _{0} - y _{1}}{x _{0} - y _{1}} = \frac{1 - 4}{( - 3 ) - 4} = \frac{3}{7} ≐ 0, 4286 α = arct g (\frac{y _{0} - y _{1}}{x _{0} - y _{1}}) = arct g (\frac{1 - 4}{( - 3 ) - 4}) ≐ 0, 4049 rad d_{x} = a \cdot cos α = 5 \cdot cos 0, 4049 ≐ 4, 5957 d_{y} = a \cdot sin α = 5 \cdot sin 0, 4049 ≐ 1, 9696 x_{2} = x_{1} + d_{y} = 1 + 1, 9696 = 2, 9696

y_{2} = y_{1} - d_{x} = 4 - 4, 5957 = - 0, 5957

x_{3} = x_{0} + d_{y} = (- 3) + 1, 9696 = - 1, 0304

y_{3} = y_{0} - d_{x} = 1 - 4, 5957 = - 3, 5957

x_{4} = x_{1} - d_{y} = 1 - 1, 9696 = - 0, 9696

y_{4} = y_{1} + d_{x} = 4 + 4, 5957 = 8, 5957

x_{5} = x_{0} - d_{y} = (- 3) - 1, 9696 = - 4, 9696

y_{5} = y_{0} + d_{x} = 1 + 4, 5957 ≐ 5, 5957 a_{2} = (x_{0} - x_{3})^{2} + (y_{0} - y_{3})^{2} = ((- 3) - (- 1, 0304))^{2} + (1 - (- 3, 5957))^{2} = 5 a_{3} = (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} = (1 - 2, 9696)^{2} + (4 - (- 0, 5957))^{2} = 5 a_{4} = (x_{2} - x_{3})^{2} + (y_{3} - y_{2})^{2} = (2, 9696 - (- 1, 0304))^{2} + ((- 3, 5957) - (- 0, 5957))^{2} = 5 b_{2} = (x_{0} - x_{5})^{2} + (y_{0} - y_{5})^{2} = ((- 3) - (- 4, 9696))^{2} + (1 - 5, 5957)^{2} = 5 b_{3} = (x_{1} - x_{4})^{2} + (y_{1} - y_{4})^{2} = (1 - (- 0, 9696))^{2} + (4 - 8, 5957)^{2} = 5 b_{4} = (x_{4} - x_{5})^{2} + (y_{4} - y_{5})^{2} = ((- 0, 9696) - (- 4, 9696))^{2} + (8, 5957 - 5, 5957)^{2} = 5

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