Questions: Find the midpoint of the segment with the following endpoints. (9,1) and (2,9)

Find the midpoint of the segment with the following endpoints. (9,1) and (2,9)
Transcript text: Find the midpoint of the segment with the following endpoints. \[ (9,1) \text { and }(2,9) \]
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Solution

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Solution Steps

To find the midpoint of a line segment with given endpoints, you can use the midpoint formula. The midpoint \((M)\) of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Solution Approach
  1. Identify the coordinates of the endpoints.
  2. Apply the midpoint formula to calculate the midpoint.
Step 1: Identify the Coordinates of the Endpoints

Given endpoints are: \[ (9, 1) \text{ and } (2, 9) \]

Step 2: Apply the Midpoint Formula

The midpoint \( M \) of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Step 3: Calculate the Midpoint

Substitute the given coordinates into the midpoint formula: \[ M = \left( \frac{9 + 2}{2}, \frac{1 + 9}{2} \right) \] \[ M = \left( \frac{11}{2}, \frac{10}{2} \right) \] \[ M = \left( 5.5, 5.0 \right) \]

Final Answer

\[ \boxed{M = \left( \frac{11}{2}, 5 \right)} \]

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