To find the midpoint between two points \((-6,7)\) and \((4,2)\), you use the midpoint formula, which is:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
For the points given:
- \(x_1 = -6\), \(y_1 = 7\)
- \(x_2 = 4\), \(y_2 = 2\)
You calculate the midpoint as follows:
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For the x-coordinates: \[ \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \]
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For the y-coordinates: \[ \frac{7 + 2}{2} = \frac{9}{2} = 4.5 \]
Thus, the midpoint is \((-1, 4.5)\).
Now, looking at the options you provided:
- No, because 7 should be added to 3, then multiplied by 2 to find the midpoint. (This statement is incorrect; it misinterprets how to find the midpoint.)
- Yes, because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates. (This statement is correct.)
- Yes, because (7 + 2) divided by 2 calculates the average, or midpoint, of the x-coordinates. (This statement is incorrect; it relates to y-coordinates.)
- No, because (7,2) is not the coordinates. (This statement is not relevant to finding the midpoint.)
The most appropriate response based on your options is: Yes, because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates.
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