Question
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(−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)
Answers
Answered by
GPT-4o mini
To find 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 \( (x_1, y_1) \) are the coordinates of point \( S \) and \( (x_2, y_2) \) are the coordinates of point \( T \).
Substituting the values:
\[
x_1 = -3, \quad y_1 = 1, \quad x_2 = 5, \quad y_2 = -4
\]
Calculating the x-coordinate of \( M \):
\[
\frac{x_1 + x_2}{2} = \frac{-3 + 5}{2} = \frac{2}{2} = 1
\]
Calculating the y-coordinate of \( M \):
\[
\frac{y_1 + y_2}{2} = \frac{1 - 4}{2} = \frac{-3}{2} = -1.5
\]
Thus, the midpoint \( M \) is:
\[
M(1, -1.5)
\]
So, the correct response is \((1, -1.5)\).
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) are the coordinates of point \( S \) and \( (x_2, y_2) \) are the coordinates of point \( T \).
Substituting the values:
\[
x_1 = -3, \quad y_1 = 1, \quad x_2 = 5, \quad y_2 = -4
\]
Calculating the x-coordinate of \( M \):
\[
\frac{x_1 + x_2}{2} = \frac{-3 + 5}{2} = \frac{2}{2} = 1
\]
Calculating the y-coordinate of \( M \):
\[
\frac{y_1 + y_2}{2} = \frac{1 - 4}{2} = \frac{-3}{2} = -1.5
\]
Thus, the midpoint \( M \) is:
\[
M(1, -1.5)
\]
So, the correct response is \((1, -1.5)\).