Question

Given the endpoints S(-3,1) and T(5,-4) calculate the midpoint

Answer 1

To calculate the midpoint \( M \) of the line segment with endpoints \( S(-3, 1) \) and \( T(5, -4) \), we 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 points \( S \) and \( T \), respectively.

Here, \( S(-3, 1) \) gives us \( x_1 = -3 \) and \( y_1 = 1 \), and \( T(5, -4) \) gives us \( x_2 = 5 \) and \( y_2 = -4 \).

Now, we can substitute these values into the midpoint formula:

\[
M = \left( \frac{-3 + 5}{2}, \frac{1 + (-4)}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{-3 + 5}{2} = \frac{2}{2} = 1
\]

Calculating the y-coordinate:

\[
\frac{1 - 4}{2} = \frac{-3}{2} = -\frac{3}{2}
\]

Thus, the midpoint \( M \) is:

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

So, the midpoint of the segment \( ST \) is \( \boxed{\left( 1, -\frac{3}{2} \right)} \).