Answer
False,
the distance is $4\sqrt{2}$.
Work Step by Step
$d(P, R)=\sqrt{(x_{2}-x_{\mathrm{I}})^{2}+(y_{2}-y_{1})^{2}}$
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$P(0,0), R(4,4),$
$d(P, R)=\sqrt{(4-0)^{2}+(4-0)^{2}}$
$=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$
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