W zadaniu korzystamy ze wzoru na odłegość między punktami A(x_A,y_A) i B(x_B,y_B):

$\left|AB\right|=\sqrt{{\left(x_B-x_A\right)}^2+{\left(y_B-y_A\right)}^2}$  

 

 

Współrzędne punktów:

$A=\left(1,2\right),B=\left(5,5\right),C=\left(3,-2\right),D=\left(-3,-1\right)$ $A=\left(1,2\right),B=\left(5,5\right),C=\left(3,-2\right),D=\left(-3,-1\right)$   

 

$\left|AB\right|=\sqrt{{\left(5-1\right)}^2+{\left(5-2\right)}^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5$  

$\left|AC\right|=\sqrt{{\left(3-1\right)}^2+{\left(-2-2\right)}^2}=\sqrt{2^2+{\left(-4\right)}^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}$   

$\left|BC\right|=\sqrt{{\left(3-5\right)}^2+{\left(-2-5\right)}^2}=\sqrt{{\left(-2\right)}^2+{\left(-7\right)}^2}=\sqrt{4+49}=\sqrt{53}$    

$\left|CD\right|=\sqrt{{\left(-3-3\right)}^2+{\left(-1-\left(-2\right)\right)}^2}=\sqrt{{\left(-6\right)}^2+1^2}=\sqrt{36+1}=\sqrt{37}$