To find the midpoint of the line segment connecting points A(-2, 2) and B(6, 5), you can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Where \((x_1, y_1)\) are the coordinates of point A and \((x_2, y_2)\) are the coordinates of point B.
For points A and B:
- A(-2, 2) → \(x_1 = -2\), \(y_1 = 2\)
- B(6, 5) → \(x_2 = 6\), \(y_2 = 5\)
To find the x-coordinate of the midpoint: \[ \frac{-2 + 6}{2} = \frac{4}{2} = 2 \]
To find the y-coordinate of the midpoint: \[ \frac{2 + 5}{2} = \frac{7}{2} = 3.5 \]
Thus, the midpoint of line segment AB is (2, 3.5).
Now, looking at your options regarding the operation of adding \(6 + 2\) and then dividing by \(2\):
- \(6 + 2\) corresponds to adding the y-coordinates of A and B, while dividing by \(2\) gives the average of those y-values. This operation \( (6 + 2)/2 \) gives:
\(\frac{2 + 5}{2} = \frac{7}{2} = 3.5\)
So, this operation finds the average of the y-values.
Given the options provided:
A. it finds the average distance between the two y-values of points A and B
B. It finds the sole midpoint of points A and B
C. It finds the average distance between the two x-values of points A and B
D. It finds the distance between points A and B
The correct choice is: A. it finds the average distance between the two y-values of points A and B.
However, it should be noted that while option A states "average distance," it should correctly refer to finding the average y-coordinate value (midpoint) rather than a physical distance.
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