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The Midpoint Formula Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. 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 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 (7,2) 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. 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 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. Skip to navigation page 14 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
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GPT-4o mini
To determine whether adding 7 + 2 and then dividing by 2 helps in finding the midpoint of the line segment JK, we need to evaluate what those numbers represent.
Assuming that 7 and 2 are the x-coordinates or the y-coordinates of points J and K, using the formula for the midpoint:
- Midpoint (M) formula for x-coordinates: \( M_x = \frac{x_1 + x_2}{2} \)
- Midpoint (M) formula for y-coordinates: \( M_y = \frac{y_1 + y_2}{2} \)
If 7 and 2 are x-coordinates (e.g., point J(7, y1) and point K(2, y2)), then:
- Adding 7 and 2 gives their total, and dividing by 2 gives the average (midpoint) of the x-coordinates of points J and K.
If 7 and 2 are y-coordinates, the reasoning is the same for determining the average of the y-coordinates.
With this in mind, the correct responses would be:
1. Yes because \( (7 + 2) ÷ 2 \) calculates the average, or midpoint, of the x-coordinates of points J and K.
or
2. Yes because \( (7 + 2) ÷ 2 \) calculates the average, or midpoint, of the y-coordinates of points J and K.
The choice depends on whether 7 and 2 actually represent x or y coordinates. However, if the question doesn't provide additional context about which specific points J and K are, it’s important to identify them in the image.
Assuming that 7 and 2 are the x-coordinates or the y-coordinates of points J and K, using the formula for the midpoint:
- Midpoint (M) formula for x-coordinates: \( M_x = \frac{x_1 + x_2}{2} \)
- Midpoint (M) formula for y-coordinates: \( M_y = \frac{y_1 + y_2}{2} \)
If 7 and 2 are x-coordinates (e.g., point J(7, y1) and point K(2, y2)), then:
- Adding 7 and 2 gives their total, and dividing by 2 gives the average (midpoint) of the x-coordinates of points J and K.
If 7 and 2 are y-coordinates, the reasoning is the same for determining the average of the y-coordinates.
With this in mind, the correct responses would be:
1. Yes because \( (7 + 2) ÷ 2 \) calculates the average, or midpoint, of the x-coordinates of points J and K.
or
2. Yes because \( (7 + 2) ÷ 2 \) calculates the average, or midpoint, of the y-coordinates of points J and K.
The choice depends on whether 7 and 2 actually represent x or y coordinates. However, if the question doesn't provide additional context about which specific points J and K are, it’s important to identify them in the image.
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