Find the midpoint of the segment with the following endpoints.

(−2,3) and (8,−2)

1 answer

To find the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), we use the midpoint formula:

\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given the endpoints \((-2, 3)\) and \((8, -2)\):

  • \(x_1 = -2\)
  • \(y_1 = 3\)
  • \(x_2 = 8\)
  • \(y_2 = -2\)

Now, we substitute these values into the formula:

\[ \text{Midpoint} = \left( \frac{-2 + 8}{2}, \frac{3 + (-2)}{2} \right) \]

Calculating the x-coordinate:

\[ \frac{-2 + 8}{2} = \frac{6}{2} = 3 \]

Calculating the y-coordinate:

\[ \frac{3 + (-2)}{2} = \frac{1}{2} = 0.5 \]

Thus, the midpoint of the segment is

\[ \boxed{(3, 0.5)} \]