Question
Q is the midpoint of line segment P (2,1) M (-2,1) . Find midpoint Q . (1 point) Responses Q is located at (1,0) . upper Q is located at left parenthesis 1 comma 0 right parenthesis . Q is located at (0.5,0) . upper Q is located at left parenthesis 0.5 comma 0 right parenthesis . Q is located at (1,6) . upper Q is located at left parenthesis 1 comma 6 right parenthesis . Q is located at (1,−6) .
Answers
GPT-4o mini
To find the midpoint \( Q \) of the line segment defined by points \( P(2,1) \) and \( M(-2,1) \), we can use the midpoint formula:
\[
Q\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points \( P \) and \( M \).
In this case:
- \( x_1 = 2, y_1 = 1 \)
- \( x_2 = -2, y_2 = 1 \)
Calculating the coordinates of midpoint \( Q \):
\[
Q_x = \frac{2 + (-2)}{2} = \frac{0}{2} = 0
\]
\[
Q_y = \frac{1 + 1}{2} = \frac{2}{2} = 1
\]
Thus, the midpoint \( Q \) is located at:
\[
Q(0, 1)
\]
However, it seems that \( Q \) being at (0,1) is not listed in your options. Double-checking the other details:
The correct answer should indeed be \( Q(0, 1) \). If that's not an option, please ensure that the original coordinates of points \( P \) and \( M \) are accurate.
If you are looking for different potential options, none of the responses given would apply to our calculation. Please verify the context, or let me know if there are any other points you'd like to check!
\[
Q\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points \( P \) and \( M \).
In this case:
- \( x_1 = 2, y_1 = 1 \)
- \( x_2 = -2, y_2 = 1 \)
Calculating the coordinates of midpoint \( Q \):
\[
Q_x = \frac{2 + (-2)}{2} = \frac{0}{2} = 0
\]
\[
Q_y = \frac{1 + 1}{2} = \frac{2}{2} = 1
\]
Thus, the midpoint \( Q \) is located at:
\[
Q(0, 1)
\]
However, it seems that \( Q \) being at (0,1) is not listed in your options. Double-checking the other details:
The correct answer should indeed be \( Q(0, 1) \). If that's not an option, please ensure that the original coordinates of points \( P \) and \( M \) are accurate.
If you are looking for different potential options, none of the responses given would apply to our calculation. Please verify the context, or let me know if there are any other points you'd like to check!