Question

Find the midpoint between (5, 2), and (–7, 8).

Answer 1

To find the midpoint between two points \((x_1, y_1)\) 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 \((5, 2)\) and \((-7, 8)\):

- \(x_1 = 5\), \(y_1 = 2\)
- \(x_2 = -7\), \(y_2 = 8\)

Now, plug these values into the formula:

\[
\text{Midpoint} = \left( \frac{5 + (-7)}{2}, \frac{2 + 8}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{5 - 7}{2} = \frac{-2}{2} = -1
\]

Calculating the y-coordinate:

\[
\frac{2 + 8}{2} = \frac{10}{2} = 5
\]

Thus, the midpoint is:

\[
\text{Midpoint} = (-1, 5)
\]

Therefore, the midpoint between \((5, 2)\) and \((-7, 8)\) is \((-1, 5)\).