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Find the midpoint of the segment with the following endpoints. (-1, -1) and (5, -5)

Check the final answer first, then review the worked steps.

Problem

Find the midpoint of the segment with the following endpoints. (-1, -1) and (5, -5)

Answer

\([2, -3]\)

Step-by-step solution

  1. Identify the Midpoint Formula: The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$
  2. Assign Coordinates: Let the first endpoint be $(x_1, y_1) = (-1, -1)$ and the second endpoint be $(x_2, y_2) = (5, -5)$.
  3. Calculate the x-coordinate of the midpoint: Substitute the x-values into the formula: $$x_m = \frac{-1 + 5}{2} = \frac{4}{2} = 2$$
  4. Calculate the y-coordinate of the midpoint: Substitute the y-values into the formula: $$y_m = \frac{-1 + (-5)}{2} = \frac{-1 - 5}{2} = \frac{-6}{2} = -3$$
  5. State the Midpoint: Combine the calculated x and y coordinates to find the midpoint: $$M = (2, -3)$$