# Coordinates of square vertices

The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.

Result

x1 =  -7
y1 =  -1
x2 =  -2
y2 =  2
x3 =  -4
y3 =  -6

#### Solution:

$s_{ 0 } = -3 \ \\ s_{ 1 } = -2 \ \\ \ \\ x_{ 0 } = 1 \ \\ y_{ 0 } = -3 \ \\ \ \\ d_{ 0 } = x_{ 0 }-s_{ 0 } = 1-(-3) = 4 \ \\ d_{ 1 } = y_{ 0 }-s_{ 1 } = (-3)-(-2) = -1 \ \\ \ \\ n \perp d \ \\ |n| = |d| \ \\ n . d = 0 \ \\ \ \\ n_{ 0 } = -d_{ 1 } = -(-1) = 1 \ \\ n_{ 1 } = d_{ 0 } = 4 \ \\ \ \\ x_{ 1 } = s_{ 0 }-d_{ 0 } = (-3)-4 = -7$
$y_{ 1 } = s_{ 1 }-d_{ 1 } = (-2)-(-1) = -1$
$x_{ 2 } = s_{ 0 }+n_{ 0 } = (-3)+1 = -2$
$y_{ 2 } = s_{ 1 }+n_{ 1 } = (-2)+4 = 2$
$x_{ 3 } = s_{ 0 }-n_{ 0 } = (-3)-1 = -4$
$y_{ 3 } = s_{ 1 }-n_{ 1 } = (-2)-4 = -6$

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