The sketch displays the curve $y = \sqrt{x - 1}$ together with the points $A(1, 0)$ and $B(5, 2)$ on it.
(i)[2]
Determine the equation of line $AB$, and express your answer in the form $y = mx + c$.
(ii)[5]
Show all necessary working to find the equation of the tangent to the curve that is parallel to $AB$.
(iii)[3]
Find the perpendicular distance between line $AB$ and the tangent parallel to $AB$. Give your answer to $2$ decimal places.
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