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)

1 answer

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 \((-4, 5)\).