Good evening ,
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Step-by-step explanation:
AO=[tex]\sqrt{p^{2}+q^{2} }[/tex]
AB=[tex]\sqrt{( p+2q-p)^{2} + (q+2p-q)^{2}[/tex]
=[tex]\sqrt{(2q)^{2}+(2p)^{2} }[/tex]
=[tex]\sqrt{4(q^{2}+p^{2} ) }[/tex]
=[tex]2\sqrt{p^{2}+q^{2} }[/tex]
=2AO.
:)
