Question
If point Q is the midpoint of segment AM, find midpoint Q.
Point a (5,2)
Point M(-2,-3)
(1 point)
Q is located at (-2.5, 3.5).
• Q is located at (- 9, — 8)
• Q is located at (1.5, 0.5).
Q s located at (12, 7)
Point a (5,2)
Point M(-2,-3)
(1 point)
Q is located at (-2.5, 3.5).
• Q is located at (- 9, — 8)
• Q is located at (1.5, 0.5).
Q s located at (12, 7)
Answers
GPT-4o mini
To find the midpoint \( Q \) of segment \( AM \) where \( A(5, 2) \) and \( M(-2, -3) \), we use the midpoint formula:
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( M \):
- \( x_1 = 5 \), \( y_1 = 2 \)
- \( x_2 = -2 \), \( y_2 = -3 \)
Now, we can substitute the coordinates into the formula:
\[
Q_x = \frac{5 + (-2)}{2} = \frac{5 - 2}{2} = \frac{3}{2} = 1.5
\]
\[
Q_y = \frac{2 + (-3)}{2} = \frac{2 - 3}{2} = \frac{-1}{2} = -0.5
\]
Therefore, the coordinates of point \( Q \) are:
\[
Q = \left( 1.5, -0.5 \right)
\]
It appears that you may have written the \( y \)-coordinate incorrectly in the options. The correct midpoint \( Q \) is \( (1.5, -0.5) \). However, based on your answer options, you only have \( (1.5, 0.5) \) listed but that is not correct. The correct answer is \( (1.5, -0.5) \).
\[
Q = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( M \):
- \( x_1 = 5 \), \( y_1 = 2 \)
- \( x_2 = -2 \), \( y_2 = -3 \)
Now, we can substitute the coordinates into the formula:
\[
Q_x = \frac{5 + (-2)}{2} = \frac{5 - 2}{2} = \frac{3}{2} = 1.5
\]
\[
Q_y = \frac{2 + (-3)}{2} = \frac{2 - 3}{2} = \frac{-1}{2} = -0.5
\]
Therefore, the coordinates of point \( Q \) are:
\[
Q = \left( 1.5, -0.5 \right)
\]
It appears that you may have written the \( y \)-coordinate incorrectly in the options. The correct midpoint \( Q \) is \( (1.5, -0.5) \). However, based on your answer options, you only have \( (1.5, 0.5) \) listed but that is not correct. The correct answer is \( (1.5, -0.5) \).