To find the total distance Paul will travel on his way home, we need to calculate the distance between each pair of locations.
Looking at the graph, we can see that the distance between Jacob's house and the grocery store is represented by the line segment connecting the two points. Similarly, the distance between the grocery store and Paul's home is represented by the line segment connecting those two points.
To calculate the distance between two points on a graph, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates of the three points on the graph:
Jacob's house: (x1, y1)
Grocery store: (x2, y2)
Paul's home: (x3, y3)
By examining the graph, we can see that Jacob's house is located at (0, 4), the grocery store is located at (3, 0), and Paul's home is located at (6, 4).
Now, we can calculate the distance between Jacob's house and the grocery store:
d1 = √((3 - 0)^2 + (0 - 4)^2)
d1 = √(9 + 16)
d1 = √25
d1 = 5
Next, we can calculate the distance between the grocery store and Paul's home:
d2 = √((6 - 3)^2 + (4 - 0)^2)
d2 = √(9 + 16)
d2 = √25
d2 = 5
Finally, we can find the total distance by adding the two distances together:
Total distance traveled = d1 + d2
Total distance traveled = 5 + 5
Total distance traveled = 10
Therefore, the total distance Paul will travel on his way home is 10.