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Part 1
Find the midpoint of the line segment with endpoints Upper P 1left parenthesis StartFraction 11 Over 2 EndFraction comma three eighths right parenthesis
and Upper P 2left parenthesis negative five halves comma five eighths right parenthesis
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Part 1
The midpoint of the line segment is
  
enter your response here.
​(Simplify your answer. Type an ordered​ pair.)

1 answer

To find the midpoint \( M \) of a line segment with endpoints \( P_1 \left( \frac{11}{2}, \frac{3}{8} \right) \) and \( P_2 \left( -\frac{5}{2}, \frac{5}{8} \right) \), we use the midpoint formula:

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

where \( (x_1, y_1) = P_1 \) and \( (x_2, y_2) = P_2 \).

Step 1: Calculate the x-coordinate of the midpoint

\[ x_1 = \frac{11}{2}, \quad x_2 = -\frac{5}{2} \]

\[ \text{Midpoint } x = \frac{\frac{11}{2} + \left( -\frac{5}{2} \right)}{2} = \frac{\frac{11 - 5}{2}}{2} = \frac{\frac{6}{2}}{2} = \frac{6}{4} = \frac{3}{2} \]

Step 2: Calculate the y-coordinate of the midpoint

\[ y_1 = \frac{3}{8}, \quad y_2 = \frac{5}{8} \]

\[ \text{Midpoint } y = \frac{\frac{3}{8} + \frac{5}{8}}{2} = \frac{\frac{3 + 5}{8}}{2} = \frac{\frac{8}{8}}{2} = \frac{1}{2} \]

Step 3: Combine the coordinates

So the midpoint \( M \) is:

\[ M = \left( \frac{3}{2}, \frac{1}{2} \right) \]

Thus, the midpoint of the line segment is

\[ \boxed{\left( \frac{3}{2}, \frac{1}{2} \right)} \]