To find the midpoint \( M \) of a line segment defined by two endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \), you can use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the coordinates of points \( J(-6, 7) \) and \( K(4, 2) \):
- The x-coordinates are \(-6\) and \(4\).
- The y-coordinates are \(7\) and \(2\).
Calculating the midpoints:
For the x-coordinates: \[ \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \]
For the y-coordinates: \[ \frac{7 + 2}{2} = \frac{9}{2} = 4.5 \]
Thus, the midpoint \( M \) is: \[ M = \left( -1, 4.5 \right) \]
Now, regarding the initial question about adding \( 7 + 2 \) and dividing by \( 2 \):
The expression \( (7 + 2) \div 2 \) indeed calculates the average of the y-coordinates of points \( J \) and \( K\), which gives \( 4.5 \) - the y-coordinate of the midpoint.
However, it does not help find the x-coordinate's midpoint since it deals specifically with the y-coordinates.
Among the provided options, the most accurate response is:
- Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.
This choice correctly identifies that the operation performed gives you the y-coordinate of the midpoint, though it is important to note that you would need to consider both x and y coordinates to fully determine the midpoint of the line segment.
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