The points a(3, 4), b(3, -2), c(-5, -2), and d(-5, 4) form rectangle abcd. which point is halfway between a and b?

   " (3,1)  is the point that is halfway between A and B. " 

Explanation:

We know that there is a "straight line segment" along the y-axis between
 "point A"  and "point B" ;  since, we are given that: 

 1)  Points A, B, C, and D form a rectangle;  AND:
 
 2) We are given the coordinates for each of the 4 (FOUR points); AND:
 
 3) The coordinates of  "Point A" (3,4)  and "Point B" (3, -2) ; have the same "x-coordinate" value.

  We are asked to find the point that is "half-way" between A and B.

  We know that the x-coordinate of this "half-way" point is three.

We can look at the "y-coordinates" of BOTH "Point A" and "Point B".

which are "4" and "-2",  respectively.

Now, let us determine the MAGNITUDE of the number of points along the "y-axis" between "y = 4" and y = -2 . 

The answer is:  "6" ;  since, from y = -2 to 0 , there are 2 points, or 2 "units" from y = -2 to y = 0 ;  then, from y = 0 to y = 4, there are 4 points, or 4 "units".

Adding these together,  2 + 4 = 6 units.

So, the "half-way" point would be 1/2  of  6 units, or 3 units.

So, from y = -2 to y = 4 ;  we could count 3 units between these points, along the "y-axis".   Note, we could count "2" units from  "y = -2"  to "y = 0". 
Then we could count one more unit, for a total of 3 units;  from y = 0 to y = 1;  and that would be the answer (y-coordinate of the point).

Alternately, or to check this answer, we could determine the "halfway" point along the "y-axis" from "y = 4" to "y = -2" ; by counting 3 units along the "y-axis" ; starting starting with "y = 4" ; note:  4 - 3 = 1 ; which is the "y-coordinate" of our answer; that is: "y = 1" ;  and the same y-coordinate we have from the previous (aforementioned) method above.

We know the "x-coordinate" is "3" ; so the

   " (3,1)  is the point that is halfway between A and B ."