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.

Correct answer:

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

Step-by-step explanation:

$$\begin{gathered} s_0=-3 \\ {s}_1=-2 \\ {x}_0=1 \\ {y}_0=-3 \\ {d}_0=x_0-s_0=1-(-3)=4 \\ {d}_1=y_0-s_1=(-3)-(-2)=-1 \\ n\perp d \\ \mathrm{\mid }n\mathrm{\mid }=\mathrm{\mid }d\mathrm{\mid } \\ n\mathrm{.}d=0 \\ {n}_0=-d_1=-(-1)=1 \\ {n}_1=d_0=4 \\ {x}_1=s_0-d_0=(-3)-4=-7 \end{gathered}$$

$y_1=s_1-d_1=(-2)-(-1)=-1$

$x_2=s_0+n_0=(-3)+1=-2$

$y_2=s_1+n_1=(-2)+4=2$

$x_3=s_0-n_0=(-3)-1=-4$

$y_3=s_1-n_1=(-2)-4=-6$

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