Question

If Paul drops the groceries he purchased halfway between the grocery store and his home, where would that location be on the graph?
home is -6,0 store is 6,3 jacobs is 4,-5


(1 point)
Responses

(0, −3/2)
(−12, 3/2)
(−6, −3/2)
(0, 3/2)

Answer 1

To find the location where Paul drops the groceries, we need to determine the midpoint between his home and the grocery store.

The coordinates of Paul's home are (-6, 0) and the coordinates of the grocery store are (6, 3).

The formula for finding the midpoint \((x_m, y_m)\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
(x_m, y_m) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Plugging in the coordinates of home and store:

\[
(x_m, y_m) = \left( \frac{-6 + 6}{2}, \frac{0 + 3}{2} \right) = \left( \frac{0}{2}, \frac{3}{2} \right) = (0, \frac{3}{2})
\]

Thus, the location where Paul drops the groceries is (0, 3/2).

The correct response is:
(0, 3/2)