a)  $A=\left(-23,62\right),B=\left(-25,54\right)$  

$M=\left(\frac{-23+\left(-25\right)}{2},\frac{62+54}{2}\right)$  

$M=\left(-24,58\right)$  

$\left|AB\right|=\sqrt{{\left(-25-\left(-23\right)\right)}^2+{\left(54-62\right)}^2}=$  

$=\sqrt{{\left(-2\right)}^2+{\left(-8\right)}^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}$  

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b)  $A=\left(90,-15\right),B=\left(102,-10\right)$  

$\mathbf{M}=\left(\frac{90+102}{2},\frac{-15+\left(-10\right)}{2}\right)$  

$\mathbf{M}=\left(96,-\frac{25}{2}\right)$  

$\left|\mathbf{A}\mathbf{B}\right|=\sqrt{{\left(102-90\right)}^2+{\left(-10-\left(-15\right)\right)}^2}=$  

$=\sqrt{{\left(12\right)}^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$  

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c)  $A=\left(-2\frac{1}{2},-40\right),B=\left(3\frac{1}{2},-42\right)$  

$\mathbf{M}=\left(\frac{-2\frac{1}{2}+3\frac{1}{2}}{2},\frac{-40+\left(-42\right)}{2}\right)$  

$\mathbf{M}=\left(\frac{1}{2},-41\right)$  

$\left|\mathbf{A}\mathbf{B}\right|=\sqrt{{\left(3\frac{1}{2}-\left(-2\frac{1}{2}\right)\right)}^2+{\left(-42-\left(-40\right)\right)}^2}=$  

$=\sqrt{6^2+{\left(-2\right)}^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}$  

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d)  $A=\left(0,90\right),B=\left(-2\sqrt{5},94\right)$  

$\mathbf{M}=\left(\frac{0+\left(-2\sqrt{5}\right)}{2},\frac{90+94}{2}\right)$  

$\mathbf{M}=\left(-\sqrt{5},92\right)$  

$\left|\mathbf{A}\mathbf{B}\right|=\sqrt{{\left(-2\sqrt{5}-0\right)}^2+{\left(94-90\right)}^2}=$  

$=\sqrt{{\left(-2\sqrt{5}\right)}^2+4^2}=\sqrt{20+16}=\sqrt{36}=6$