Question
Q is the midpoint of line segment PM¯¯¯¯¯¯¯¯¯ . 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 (1,6) . upper Q is located at left parenthesis 1 comma 6 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) .
Answers
Answer
P is, (1,2) M is, (1,-2)
Answered by
GPT-4o mini
To find the midpoint \( Q \) of the line segment \( PM \), we need the coordinates of points \( P \) and \( M \). The midpoint \( Q \) can be calculated using the formula:
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) are the coordinates of point \( P \), and \( (x_2, y_2) \) are the coordinates of point \( M \).
However, since we do not have the coordinates of points \( P \) and \( M \) provided in your question, we cannot directly calculate the coordinates of midpoint \( Q \).
If you have specific coordinates for points \( P \) and \( M \), please provide them, and I can help calculate the midpoint \( Q \). Without that information, I cannot determine which one of the provided responses is correct.
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
where \( (x_1, y_1) \) are the coordinates of point \( P \), and \( (x_2, y_2) \) are the coordinates of point \( M \).
However, since we do not have the coordinates of points \( P \) and \( M \) provided in your question, we cannot directly calculate the coordinates of midpoint \( Q \).
If you have specific coordinates for points \( P \) and \( M \), please provide them, and I can help calculate the midpoint \( Q \). Without that information, I cannot determine which one of the provided responses is correct.
Answered by
GPT-4o mini
Given the coordinates of points \( P(1, 2) \) and \( M(1, -2) \), we can find the midpoint \( Q \) using the midpoint formula:
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substituting the coordinates of \( P \) and \( M \):
\[
Q = \left( \frac{1 + 1}{2}, \frac{2 + (-2)}{2} \right)
\]
Calculating the components:
\[
Q = \left( \frac{2}{2}, \frac{0}{2} \right) = (1, 0)
\]
So, the midpoint \( Q \) is located at \( (1, 0) \).
The correct response is: **Q is located at (1, 0).**
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substituting the coordinates of \( P \) and \( M \):
\[
Q = \left( \frac{1 + 1}{2}, \frac{2 + (-2)}{2} \right)
\]
Calculating the components:
\[
Q = \left( \frac{2}{2}, \frac{0}{2} \right) = (1, 0)
\]
So, the midpoint \( Q \) is located at \( (1, 0) \).
The correct response is: **Q is located at (1, 0).**
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