Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, 2, comma, 1, right parenthesis, and , left parenthesis, 10, comma, 6, right parenthesis
(2,1) and (10,6)

Answer 1

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

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

Given the points \((2, 1)\) and \((10, 6)\):
- \(x_1 = 2\), \(y_1 = 1\)
- \(x_2 = 10\), \(y_2 = 6\)

Now, plug the values into the formula:

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

Calculating the \(x\) component:
\[
\frac{2 + 10}{2} = \frac{12}{2} = 6
\]

Calculating the \(y\) component:
\[
\frac{1 + 6}{2} = \frac{7}{2} = 3.5
\]

So, the midpoint of the segment is \(\left( 6, 3.5 \right)\).