Question
Question
Use the image to answer the question.
Line segment upper J upper K slants down left to right on a coordinate plane. The x-axis ranges from negative 7 to 5 and y-axis ranges from 0 to 8 both in 1 unit increments.
Does adding 7+2
and then dividing by 2 help you find the find midpoint of line segment JK¯¯¯¯¯¯¯¯
?
(1 point)
Responses
Yes because (7+2)÷2
calculates the average, or midpoint, of the x-coordinates of points J and K.
Yes because open paren 7 plus 2 close paren divided by 2 calculates the average, or midpoint, of the x -coordinates of points J and K.
No because (7,2)
is not the coordinate of point J or K.
No because open paren 7 comma 2 close paren is not the coordinate of point J or K.
Yes because (7+2)÷2
calculates the average, or midpoint, of the y-coordinates of points J and K.
Yes because open paren 7 plus 2 close paren divided by 2 calculates the average, or midpoint, of the y -coordinates of points J and K.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
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Use the image to answer the question.
Line segment upper J upper K slants down left to right on a coordinate plane. The x-axis ranges from negative 7 to 5 and y-axis ranges from 0 to 8 both in 1 unit increments.
Does adding 7+2
and then dividing by 2 help you find the find midpoint of line segment JK¯¯¯¯¯¯¯¯
?
(1 point)
Responses
Yes because (7+2)÷2
calculates the average, or midpoint, of the x-coordinates of points J and K.
Yes because open paren 7 plus 2 close paren divided by 2 calculates the average, or midpoint, of the x -coordinates of points J and K.
No because (7,2)
is not the coordinate of point J or K.
No because open paren 7 comma 2 close paren is not the coordinate of point J or K.
Yes because (7+2)÷2
calculates the average, or midpoint, of the y-coordinates of points J and K.
Yes because open paren 7 plus 2 close paren divided by 2 calculates the average, or midpoint, of the y -coordinates of points J and K.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
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Answers
GPT-4o mini
To determine if adding \(7 + 2\) and then dividing by \(2\) helps you find the midpoint of line segment \(JK\), we need to consider what points \(J\) and \(K\) could represent and how midpoints are calculated.
The midpoint \(M\) of a line segment defined by two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
1. If \(7\) and \(2\) represent the x-coordinates of points \(J\) and \(K\), then calculating \((7 + 2) / 2\) would provide the x-coordinate of the midpoint.
2. However, if \(7\) and \(2\) do not correspond to the x-coordinates of points \(J\) and \(K\) as per the given scenario, then using these values would not yield the correct midpoint.
3. It's also crucial to consider the context of the other response options that imply whether \(7\) or \(2\) represents coordinates pertaining to \(J\) or \(K\), which seems not to align given the information provided (“No because \( (7,2) \) is not the coordinate of point \(J\) or \(K\)”).
Thus, judging by the above analysis, the most accurate responses to follow from the problem statement are:
- **No because \( (7, 2) \) is not the coordinate of point \(J\) or \(K\).**
This option accurately reflects that using coordinates that do not belong to the endpoints will yield incorrect results regarding finding the midpoint.
The midpoint \(M\) of a line segment defined by two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
1. If \(7\) and \(2\) represent the x-coordinates of points \(J\) and \(K\), then calculating \((7 + 2) / 2\) would provide the x-coordinate of the midpoint.
2. However, if \(7\) and \(2\) do not correspond to the x-coordinates of points \(J\) and \(K\) as per the given scenario, then using these values would not yield the correct midpoint.
3. It's also crucial to consider the context of the other response options that imply whether \(7\) or \(2\) represents coordinates pertaining to \(J\) or \(K\), which seems not to align given the information provided (“No because \( (7,2) \) is not the coordinate of point \(J\) or \(K\)”).
Thus, judging by the above analysis, the most accurate responses to follow from the problem statement are:
- **No because \( (7, 2) \) is not the coordinate of point \(J\) or \(K\).**
This option accurately reflects that using coordinates that do not belong to the endpoints will yield incorrect results regarding finding the midpoint.