# Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.

Result

x2 =  2.97
y2 =  -0.596
x3 =  -1.03
y3 =  -3.596
x4 =  -0.97
y4 =  8.596
x5 =  -4.97
y5 =  5.596

#### Solution:

$x_{ 0 } = -3 \ \\ y_{ 0 } = 1 \ \\ \ \\ x_{ 1 } = 1 \ \\ y_{ 1 } = 4 \ \\ \ \\ a = \sqrt{ (x_{ 0 }-x_{ 1 })^2+(y_{ 0 }-y_{ 1 })^2 } = \sqrt{ ((-3)-1)^2+(1-4)^2 } = 5 \ \\ \ \\ \tan α = \dfrac{ y_{ 0 }-y_{ 1 } }{ x_{ 0 }-y_{ 1 } } = \dfrac{ 1-4 }{ (-3)-4 } = \dfrac{ 3 }{ 7 } \doteq 0.4286 \ \\ \ \\ α = \arctan (\dfrac{ y_{ 0 }-y_{ 1 } }{ x_{ 0 }-y_{ 1 } } ) = \arctan (\dfrac{ 1-4 }{ (-3)-4 } ) \doteq 0.4049 \ rad \ \\ \ \\ dx = a \cdot \ \cos(α) = 5 \cdot \ \cos(0.4049) \doteq 4.5957 \ \\ dy = a \cdot \ \sin(α) = 5 \cdot \ \sin(0.4049) \doteq 1.9696 \ \\ \ \\ x_{ 2 } = x_{ 1 } + dy = 1 + 1.9696 \doteq 2.9696 = 2.97$
$y_{2} =y_{ 2 } = y_{ 1 } - dx = 4 - 4.5957 \doteq -0.5957 = -0.596$
$x_{ 3 } = x_{ 0 } + dy = (-3) + 1.9696 \doteq -1.0304 = -1.03$
$y_{ 3 } = y_{ 0 } - dx = 1 - 4.5957 \doteq -3.5957 = -3.596$
$x_{4} =x_{ 4 } = x_{ 1 } - dy = 1 - 1.9696 \doteq -0.9696 = -0.97$
$y_{4} =y_{ 4 } = y_{ 1 } + dx = 4 + 4.5957 \doteq 8.5957 = 8.596$
$x_{ 5 } = x_{ 0 } - dy = (-3) - 1.9696 \doteq -4.9696 = -4.97$
$y_{ 5 } = y_{ 0 } + dx = 1 + 4.5957 \doteq 5.5957= 5.596 \ \\ \ \\ a_{ 2 } = \sqrt{ (x_{ 0 }-x_{ 3 })^2+(y_{ 0 }-y_{ 3 })^2 } = \sqrt{ ((-3)-(-1.0304))^2+(1-(-3.5957))^2 } \doteq 5.0004 \ \\ a_{ 3 } = \sqrt{ (x_{ 1 }-x_{ 2 })^2+(y_{ 1 }-y_{ 2 })^2 } = \sqrt{ (1-2.9696)^2+(4-(-0.5957))^2 } \doteq 5.0004 \ \\ a_{ 4 } = \sqrt{ (x_{ 2 }-x_{ 3 })^2+(y_{ 3 }-y_{ 2 })^2 } = \sqrt{ (2.9696-(-1.0304))^2+((-3.5957)-(-0.5957))^2 } = 5 \ \\ \ \\ b_{ 2 } = \sqrt{ (x_{ 0 }-x_{ 5 })^2+(y_{ 0 }-y_{ 5 })^2 } = \sqrt{ ((-3)-(-4.9696))^2+(1-5.5957)^2 } \doteq 5.0002 \ \\ b_{ 3 } = \sqrt{ (x_{ 1 }-x_{ 4 })^2+(y_{ 1 }-y_{ 4 })^2 } = \sqrt{ (1-(-0.9696))^2+(4-8.5957)^2 } \doteq 5.0004 \ \\ b_{ 4 } = \sqrt{ (x_{ 4 }-x_{ 5 })^2+(y_{ 4 }-y_{ 5 })^2 } = \sqrt{ ((-0.9696)-(-4.9696))^2+(8.5957-5.5957)^2 } \doteq 5.0002$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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