Question

In the standard (x, y) coordinate plane, what is the midpoint of the line segment with endpoints at (-5, 4) and (-3, 6)?

(4, -5)

(5, -4)

(-4, 5)

(-5, 4)

(-1, 8)

Answer 1

To find the midpoint of a line segment with endpoints \((-5, 4)\) and \((-3, 6)\), we can use the midpoint formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

In this case:
- \((x_1, y_1) = (-5, 4)\)
- \((x_2, y_2) = (-3, 6)\)

Now substituting these values into the midpoint formula:

\[
\text{Midpoint} = \left( \frac{-5 + (-3)}{2}, \frac{4 + 6}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{-5 - 3}{2} = \frac{-8}{2} = -4
\]

Calculating the y-coordinate:

\[
\frac{4 + 6}{2} = \frac{10}{2} = 5
\]

Thus, the midpoint of the line segment is:

\[
(-4, 5)
\]

Therefore, the answer is \((-4, 5)\).