If Paul drops the groceries he purchased halfway between the grocery store and his home, where would that location be on the graph?

Question

home is -6,0 store is 6,3 jacobs is 4,-5

(1 point)
Responses

(0, −32)
(0, −32)

(−12, 32)
(−12, 32)

(−6, −32)
(−6, −32)

(0, 32)

Answer 1

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

Paul's home is at the coordinates (-6, 0) and the grocery store is at (6, 3).

The formula for finding the midpoint (M) between two points (x1, y1) and (x2, y2) is:

\[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]

Substituting in the coordinates of home and store:

• \( x1 = -6 \)
• \( y1 = 0 \)
• \( x2 = 6 \)
• \( y2 = 3 \)

Calculating the x-coordinate of the midpoint:

\[ M_x = \frac{-6 + 6}{2} = \frac{0}{2} = 0 \]

Calculating the y-coordinate of the midpoint:

\[ M_y = \frac{0 + 3}{2} = \frac{3}{2} = 1.5 \]

Thus, the midpoint is (0, 1.5).

However, none of the options provided matches (0, 1.5). Based on the options provided, there seems to be an error or misunderstanding, as none of the given choices represent the correct midpoint or make geographical sense according to the coordinates provided.

Please re-check the question or options.