Question

Use the image to answer the question.

A line segment on a coordinate plane. The x-asis ranges from negative 4 to 7 in unit increments. The y-axis ranges from negative 5 to 2 in unit increments. The line extends downward from point upper S on the top left to point upper T on the bottom right.

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

(1 point)
Responses

(1,−1.5)
left parenthesis 1 comma negative 1.5 right parenthesis

(−1,0.5)
left parenthesis negative 1 comma 0.5 right parenthesis

(−4,2.5)
left parenthesis negative 4 comma 2.5 right parenthesis

(2,−3)
left parenthesis 2 comma negative 3 right parenthesis
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Answer 1

To calculate the midpoint \( M \) of a line segment with endpoints \( S(-3, 1) \) and \( T(5, -4) \), we use the midpoint formula:

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

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

Now, we can plug these values into the formula:

1. Calculate the x-coordinate of the midpoint:
\[
\frac{-3 + 5}{2} = \frac{2}{2} = 1
\]

2. Calculate the y-coordinate of the midpoint:
\[
\frac{1 + (-4)}{2} = \frac{1 - 4}{2} = \frac{-3}{2} = -1.5
\]

Thus, the midpoint \( M \) is:

\[
M = (1, -1.5)
\]

So the correct answer is \( \left( 1, -1.5 \right) \).