Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, minus, 6, comma, minus, 6, right parenthesis, and , left parenthesis, 1, comma, minus, 3, right parenthesis
(−6,−6) and (1,−3)

Answer 1

To find the midpoint of the segment with endpoints \((-6, -6)\) and \((1, -3)\), you can use the midpoint formula:

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

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

Here, the coordinates are:
- \(x_1 = -6\), \(y_1 = -6\)
- \(x_2 = 1\), \(y_2 = -3\)

Now plug these values into the formula:

\[
M = \left( \frac{-6 + 1}{2}, \frac{-6 + (-3)}{2} \right)
\]

Calculating the x-coordinate of the midpoint:

\[
\frac{-6 + 1}{2} = \frac{-5}{2} = -2.5
\]

Calculating the y-coordinate of the midpoint:

\[
\frac{-6 - 3}{2} = \frac{-9}{2} = -4.5
\]

Therefore, the midpoint \(M\) is:

\[
M = \left(-2.5, -4.5\right)
\]

Thus, the midpoint of the segment is \(\boxed{(-2.5, -4.5)}\).