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.
(1 point)
Responses
517−−√
5 square root of 17
217−−√
2 square root of 17
317−−√
3 square root of 17
617−−√
To find the total distance Paul will travel on his way home, we need to calculate the distance between each location and add them up.
From Paul's friend Jacob's house to the grocery store:
This distance is represented by 2 times the square root of 17.
From the grocery store to Paul's house (home):
This distance is also represented by 3 times the square root of 17.
Thus, the total distance Paul will travel on his way home is 2 times the square root of 17 plus 3 times the square root of 17, which simplifies to 5 times the square root of 17.
Therefore, the correct option is 5 square root of 17.
If Paul drops the groceries he purchased halfway between the grocery store and his home, where would that location be on the graph?
(1 point)
Responses
(0, 32)
(0, 32)
(−12, 32)
(−12, 32)
(0, −32)
(0, −32)
(−6, −32)
(−6, −32)
To determine where the location would be on the graph, we need to find the midpoint between the grocery store and Paul's home.
The x-coordinate of the midpoint can be found by taking the average of the x-coordinates of the grocery store (0) and Paul's home (-6). The average is (-6 + 0)/2 = -6/2 = -3.
The y-coordinate of the midpoint can be found by taking the average of the y-coordinates of the grocery store (-32) and Paul's home (-32). The average is (-32 + (-32))/2 = -64/2 = -32.
Therefore, the location where Paul would drop the groceries halfway between the grocery store and his home would be (-3, -32).
Thus, the correct option is (−3, −32).
If Paul drops the groceries he purchased halfway between the grocery store and his home, where would that location be on the graph?
(1 point)
Responses
(0, 3/2)
(−12, 3/2)
(0, −3/2)
(−6, −3/2)
To determine where the location would be on the graph, we need to find the midpoint between the grocery store and Paul's home.
The x-coordinate of the midpoint can be found by taking the average of the x-coordinates of the grocery store (0) and Paul's home (-6). The average is (-6 + 0)/2 = -6/2 = -3.
The y-coordinate of the midpoint can be found by taking the average of the y-coordinates of the grocery store (0) and Paul's home (-3/2). The average is (0 + (-3/2))/2 = -3/4.
Therefore, the location where Paul would drop the groceries halfway between the grocery store and his home would be (-3, -3/2).
Thus, the correct option is (−3, −3/2).
To find the total distance Paul will travel on his way home, we need to add up the distances between the three locations.
From Paul's friend Jacob's house to the grocery store, the distance is represented by the blue line segment. Let's call this distance "a".
From the grocery store to Paul's house, the distance is represented by the red line segment. Let's call this distance "b".
Therefore, the total distance Paul will travel is "a + b".
Looking at the graph above, we can see that the blue line segment represents 3 times the square root of 17 (√17). Let's call this distance "a".
Similarly, the red line segment represents 2 times the square root of 17 (√17). Let's call this distance "b".
Therefore, the total distance Paul will travel is "a + b" which equals 3√17 + 2√17.
To simplify, we can combine like terms: 3√17 + 2√17 = (3 + 2)√17 = 5√17.
Hence, the total distance Paul will travel on his way home is 5 times the square root of 17 (√17). Therefore, the answer is:
5√17.
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.