Paul's mom asks him to stop at the grocery store on his way home from his friend Jacob's house to pick up some ingredients she needs for dinner. The graph below shows the location of all three places Paul will be this afternoon. Find the total distance Paul will travel on his way home.

Question

(1 point)
Responses

317−−√
3 square root of 17

617−−√
6 square root of 17

217−−√
2 square root of 17

517−−√

Answer 1

To solve the problem, we need to determine the distance Paul will travel from Jacob's house to the grocery store and then from the grocery store to his home.

Let’s denote:

• $J$ as the location of Jacob's house
• $G$ as the location of the grocery store
• $H$ as Paul’s home

Let’s assume the coordinates of these locations are:

• Jacob's house $J(x_J,y_J)$
• Grocery store $G(x_G,y_G)$
• Paul’s home $H(x_H,y_H)$

The total distance $D$ Paul travels is the sum of the distance from Jacob's house to the grocery store and from the grocery store to home:

$$D=\text{Distance from }J\text{ to }G+\text{Distance from }G\text{ to }H$$

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is calculated using the distance formula:

$$\text{Distance}=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$$

To determine the total distance, we would need the coordinates $(x_J,y_J),(x_G,y_G),(x_H,y_H)$ of Jacob's house, the grocery store, and Paul's home respectively.

Since I cannot see the graph or the specific coordinates, I cannot compute the exact distances. However, you can proceed as follows:

1. Calculate the distance $D_{JG}$ from Jacob's house $J$ to the grocery store $G$ using the distance formula.
2. Calculate the distance $D_{GH}$ from the grocery store $G$ to Paul's house $H$ using the distance formula.
3. Sum both distances to find the total travel distance $D=D_{JG}+D_{GH}$.

Once you calculate that, compare the result with the options given:

• $3\sqrt{17}$
• $6\sqrt{17}$
• $2\sqrt{17}$
• $5\sqrt{17}$

Please provide the coordinates or any visual data from the graph, and I can help further with the calculations.