Question

Given the endpoints S(−3,1) and T(5,−4) , calculate midpoint M .

Answer 1

To find the midpoint \( M \) of the line segment connecting the points \( S(x_1, y_1) \) and \( T(x_2, y_2) \), you can use the midpoint formula:

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

Given the points \( S(-3, 1) \) and \( T(5, -4) \):

- \( x_1 = -3 \), \( y_1 = 1 \)
- \( x_2 = 5 \), \( y_2 = -4 \)

Substituting the values into the 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:

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

So, the final result is:

\[
M(1, -1.5)
\] or \( M(1, -\frac{3}{2})\).