The curve is given by $y = x^2 - 4x + 4$ and the line is given by $y = mx$, with $m$ as a constant.
(i)[4]
When $m = 1$, the curve and the line meet at the points $A$ and $B$. Determine the coordinates of the midpoint of $AB$.
(ii)[5]
Determine the non-zero value of $m$ for which the line is tangent to the curve, and calculate the coordinates of the point where the tangent touches the curve.
Worked solution & mark scheme
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