Question

Find the midpoint of the segment with the following endpoints.
(10,4) and (4,10)

Answer 1

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

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

For the given points \((10, 4)\) and \((4, 10)\):

- \(x_1 = 10\), \(y_1 = 4\)
- \(x_2 = 4\), \(y_2 = 10\)

Now, substitute these values into the midpoint formula:

\[
\text{Midpoint} = \left( \frac{10 + 4}{2}, \frac{4 + 10}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{10 + 4}{2} = \frac{14}{2} = 7
\]

Calculating the y-coordinate:

\[
\frac{4 + 10}{2} = \frac{14}{2} = 7
\]

Thus, the midpoint is:

\[
\boxed{(7, 7)}
\]