Question
Does adding 7+2 and then dividing by 2 help you find the find midpoint of line segment JK¯¯¯¯¯¯¯¯? (1 point) Responses 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 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 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. Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.
Answers
Answered by
GPT-4o mini
To determine whether adding \(7\) and \(2\) and then dividing by \(2\) helps find the midpoint of a line segment \(JK\), we need to consider what the midpoint is and the context in which the coordinates \( (7, 2) \) are used.
The midpoint \(M\) of a line segment with endpoints \(J(x_1, y_1)\) and \(K(x_2, y_2)\) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Based on the given choices:
- If \(7\) and \(2\) are the \(x\)-coordinates of points \(J\) and \(K\), then calculating \((7 + 2) \div 2\) indeed provides the average of the \(x\)-coordinates, which corresponds to the \(x\)-coordinate of the midpoint \(M\).
Similarly, if \(7\) and \(2\) are the \(y\)-coordinates of points \(J\) and \(K\), then \((7 + 2) \div 2\) yields the average of the \(y\)-coordinates.
Therefore, the most appropriate responses are:
- **Yes because (7+2)÷2 calculates the average, or midpoint, of the x-coordinates of points J and K.**
- **Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.**
The correct interpretation depends on whether \(7\) and \(2\) represent the \(x\)-coordinates or \(y\)-coordinates. Without additional information about which specific coordinates \(7\) and \(2\) refer to, both options are valid depending on the context.
The midpoint \(M\) of a line segment with endpoints \(J(x_1, y_1)\) and \(K(x_2, y_2)\) is calculated using the formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Based on the given choices:
- If \(7\) and \(2\) are the \(x\)-coordinates of points \(J\) and \(K\), then calculating \((7 + 2) \div 2\) indeed provides the average of the \(x\)-coordinates, which corresponds to the \(x\)-coordinate of the midpoint \(M\).
Similarly, if \(7\) and \(2\) are the \(y\)-coordinates of points \(J\) and \(K\), then \((7 + 2) \div 2\) yields the average of the \(y\)-coordinates.
Therefore, the most appropriate responses are:
- **Yes because (7+2)÷2 calculates the average, or midpoint, of the x-coordinates of points J and K.**
- **Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.**
The correct interpretation depends on whether \(7\) and \(2\) represent the \(x\)-coordinates or \(y\)-coordinates. Without additional information about which specific coordinates \(7\) and \(2\) refer to, both options are valid depending on the context.
Answer
Answer
Answered by
GPT-4o mini
The best response is:
**Yes because (7 + 2) ÷ 2 calculates the average, or midpoint, of the x-coordinates of points J and K.**
(Note: This assumes that \(7\) and \(2\) refer to the \(x\)-coordinates of points \(J\) and \(K\). If they refer to the \(y\)-coordinates, the corresponding option would also be a correct answer.)
**Yes because (7 + 2) ÷ 2 calculates the average, or midpoint, of the x-coordinates of points J and K.**
(Note: This assumes that \(7\) and \(2\) refer to the \(x\)-coordinates of points \(J\) and \(K\). If they refer to the \(y\)-coordinates, the corresponding option would also be a correct answer.)