Find the x value for the point that splits segment ab in half if point a is located at (4, 3) and point b is located at (−2, 6).

The answer is:  "1" .

Explanation:

To start, we find this coordinates of this "point that splits the segment in half", known as the "half-point"; or, even more formally, known as the "midpoint",  using the following "midpoint formula"; in which "M" refers to the "midpoint":

Given two coordinates (points) on a (straight line segment): 

(x₁, y₁) ; AND:  (x₂ ,y₂ ) ;  

The midpoint , "M":

M = (x₁ + x₂) / 2  , (y₁ + y₂) / 2  ;


in which:   " (x₁ + x₂) / 2 " ; refers to the "x-coordinate" of the midpoint;
 
AND:        "(y₁ + y ₂) / 2 " ; refers to the "y-coordinate" of the midpoint;

       If given two particular points, use can use point to start with, as long os the second one is used for the next one:

So, given:  Point A:  (4,3) ;  4 = x₁ ; 3 = y₁ ;
                  Pont B:  (-2,6)   -2 = x₂ ; 6 = y₂ ;

 The midpoint , "M":

M = (x₁ + x₂) / 2  , (y₁ + y₂) / 2 = ?  Substitute the values:

M = [4 +(-2)] / 2 , (3 + 6) / 2 ;
  
→    [(4 − 2) / 2 ] , [(3+6) / 2 ] ;

→ (2/2), (9/2) ; 

→ (1, 4.5)

The midpoint is: (1, 4.5).  This very question asks to find the "x-value" of the midpoint, which is "1" .  (Since:  x =1, y = 4.5).   

So, the answer is: "1" .

                    

Round it to the nearest tenth