All they are asking you to do is to find the slope between the points. Here is the slope formula, where coordinates are (x₁,y₁) and (x₂,y₂): m= (y₂-y₁)/(x₂-x₁)
For example, [tex] m_a_b [/tex] is the slope between point A and point B. Here are the answers:
[tex] m_a_b [/tex] = (2 - -2)/(1 - 3) = 4/-2 = -2
[tex] m_b_c [/tex] = (3-2)/(3-1) = 1/2
[tex] m_c_d [/tex] = (-1-3)/(5-3) = -4/2 = -2
[tex] m_d_a [/tex] = (-2 - -1)/(3-5) = -1/-2 = 1/2
Since slopes on opposite sides are equal, that means we have two pairs of parallel sides, which makes up a rectangle.
