To identify where Paul drops the groceries on the graph, we would need to know the coordinates of both the grocery store and his home. Assuming that the grocery store is at the point (0, 32) and his home is at the point (0, -32), which is common in coordinate problems where the y-axis represents vertical distance from a specific reference point:
- The grocery store is at (0, 32).
- His home is at (0, -32).
If Paul drops the groceries halfway between these two locations, we can calculate the midpoint. The midpoint formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
In this case:
\[ x_1 = 0, \quad y_1 = 32 \] \[ x_2 = 0, \quad y_2 = -32 \]
Calculating the midpoint:
\[ \left( \frac{0 + 0}{2}, \frac{32 + (-32)}{2} \right) = \left( 0, \frac{0}{2} \right) = (0, 0) \]
However, if we're considering any of the given answer options (0, 32), (−6, −32), (−12, 32), and (0, −32), none of these appear to be the correct midpoint based on standard coordinate interpretations.
If you could clarify the positions of the grocery store and home on the graph, I could provide a more accurate answer. If, however, the problem assumes different defined points, please specify those points so that we can determine the location correctly.
For clarity, given the mathematical insight, if the expected option were the midpoint we calculated, it would be (0, 0).
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