Let ABCD be a rectangle with vertices A(2,3), B(8,3), C(8,−4) and D(2,−4).
(i) Show that AB and CD are horizontal lines. Find their equations and slopes.
(ii) Show that BC and AD are vertical lines. Find their equations and slopes.
(iii) Using the results obtained, calculate the perimeter and the area of the rectangle.
(iv) If E is the midpoint of side AD, write the equation of the line passing through E and parallel to AB.