Analytical geometry, help with 1 -3.5, the whole question

Here are the solutions for questions 1 to 3.5.

1. Prove whether or not ABCD is a rectangle.
To determine if ABCD is a rectangle, we can check if its opposite sides are parallel and if adjacent sides are perpendicular. This can be done by calculating the slopes of all sides.

Step 1: Calculate the slopes of the sides.
The coordinates are A(-7, 2), B(3, 6), C(6, 3), D(-4, 8).
The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope of AB ($m_{AB}$):

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