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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. S(-3,1) T(5,-4)

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

(1 point)
Responses

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

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

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

(1,−1.5)

Answer 1

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

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

where \( (x_1, y_1) \) are the coordinates of point \( S \) and \( (x_2, y_2) \) are the coordinates of point \( T \).

Substituting in the values:

\[ x_1 = -3, \quad y_1 = 1, \quad x_2 = 5, \quad y_2 = -4 \]

Calculating the midpoint:

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

\[ M_y = \frac{1 + (-4)}{2} = \frac{1 - 4}{2} = \frac{-3}{2} = -1.5 \]

Thus, the midpoint \( M \) is:

\[ M(1, -1.5) \]

The correct response is:

\((1, -1.5)\)