Find the midpoint of the segment with the following endpoints.

(2,1) and (10,6)

1 answer

To find the midpoint of a segment defined by two endpoints \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:

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

For the given endpoints \((2, 1)\) and \((10, 6)\):

  • \(x_1 = 2\)
  • \(y_1 = 1\)
  • \(x_2 = 10\)
  • \(y_2 = 6\)

Now, plug these values into the midpoint formula:

\[ \text{Midpoint} = \left( \frac{2 + 10}{2}, \frac{1 + 6}{2} \right) \]

Calculating the \(x\) coordinate:

\[ \frac{2 + 10}{2} = \frac{12}{2} = 6 \]

Calculating the \(y\) coordinate:

\[ \frac{1 + 6}{2} = \frac{7}{2} = 3.5 \]

Thus, the midpoint of the segment with endpoints \((2, 1)\) and \((10, 6)\) is:

\[ \boxed{(6, 3.5)} \]