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:
- Calculate the distance \( D_{JG} \) from Jacob's house \( J \) to the grocery store \( G \) using the distance formula.
- Calculate the distance \( D_{GH} \) from the grocery store \( G \) to Paul's house \( H \) using the distance formula.
- 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.
3 answers