To find the midpoint between two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the points \((5, 2)\) and \((-7, 8)\):
- \(x_1 = 5\), \(y_1 = 2\)
- \(x_2 = -7\), \(y_2 = 8\)
Now, plug these values into the formula:
\[ \text{Midpoint} = \left( \frac{5 + (-7)}{2}, \frac{2 + 8}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{5 - 7}{2} = \frac{-2}{2} = -1 \]
Calculating the y-coordinate:
\[ \frac{2 + 8}{2} = \frac{10}{2} = 5 \]
Thus, the midpoint is:
\[ \text{Midpoint} = (-1, 5) \]
Therefore, the midpoint between \((5, 2)\) and \((-7, 8)\) is \((-1, 5)\).