To find the midpoint between two points [tex]\((-4, 4)\)[/tex] and [tex]\( (2, -4) \)[/tex], we use the midpoint formula. The midpoint formula is given by:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Let's identify the coordinates of the given points:
- The coordinates of the first point are [tex]\( (x_1, y_1) = (-4, 4) \)[/tex]
- The coordinates of the second point are [tex]\( (x_2, y_2) = (2, -4) \)[/tex]
Now, substitute these coordinates into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-4 + 2}{2} = \frac{-2}{2} = -1 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{4 + (-4)}{2} = \frac{0}{2} = 0 \][/tex]
Therefore, the midpoint between the points [tex]\((-4, 4)\)[/tex] and [tex]\( (2, -4) \)[/tex] is:
[tex]\[ (-1, 0) \][/tex]
Thus, the correct answer is:
[tex]\[ (-1, 0) \][/tex]
