Answer
$\sqrt {95}$ units
Work Step by Step
Let $P=(x_{1},y_{1})=(-2\sqrt 5,\sqrt {10})$ and $Q=(x_{2},y_{2})=(-\sqrt 5,4\sqrt {10})$
Finding the distance between P and Q,
$d(P,Q)=\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
$d(P,Q)=\sqrt {(-\sqrt 5-(-2\sqrt 5))^{2}+(4\sqrt {10}-\sqrt {10})^{2}}$
$d(P,Q)=\sqrt {(-\sqrt 5+2\sqrt 5))^{2}+(3\sqrt {10})^{2}}$
$d(P,Q)=\sqrt {(\sqrt 5)^{2}+(3\sqrt {10})^{2}}$
$d(P,Q)=\sqrt {5+9(10)}$
$d(P,Q)=\sqrt {95}$ units