To find the midpoint of a line segment defined by two points, you take the average of the x-coordinates and the average of the y-coordinates of those points.
For points J (-6, 7) and K (4, 2):
- The x-coordinates are -6 and 4.
- The y-coordinates are 7 and 2.
To calculate the midpoint:
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For the x-coordinates: \[ \text{Midpoint x} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \]
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For the y-coordinates: \[ \text{Midpoint y} = \frac{7 + 2}{2} = \frac{9}{2} = 4.5 \]
Putting it all together, the midpoint M is at (-1, 4.5).
Now, examining the options:
A. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K. (This is correct for the y-coordinates.)
B. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the x-coordinates of points J and K. (This is incorrect; it refers to y-coordinates, not x-coordinates.)
C. No because 7 should be added to 3, then multiplied by 2 to find the midpoint. (This is incorrect; it's not the correct method for finding the midpoint.)
D. No because (7, 2) is not the coordinate of point J or K. (This is incorrect, but it is irrelevant to the method of finding the midpoint.)
The best answer is: A. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K.
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