Part 1: Abigail lives at the point (-3, -1) and wants to travel to her friend Clara's house at (2, 3) on the map. She has two choices to get there: either travel directly to Clara's house, or Abigail can stop by Bob's Store at (2, -1) to pick up snacks before travelling to Clara's house. Abigail wants to compare the two distances of her choices.A drawing of the story problem. Abigail lives at point A(-3, -1), Clara lives at point C(2, 3) and Bob's Store is at point B(2, -1). The three points form a right triangle.



a2+b2=c2


(3 points)
How long is the distance traveled if Abigail stops by Bob's Store before going to Clara's house?
units.
Question 2
Part 2: Now determine the distance traveled if Abigail goes directly to Clara's house. What is the difference in measurement between the two routes Abigail can take, and which is faster? You must show all work for full credit. (12 points)

3 answers

To find the distance traveled if Abigail stops by Bob's Store before going to Clara's house, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)

First, let's find the distance from Abigail's house to Bob's Store:
distance_AB = √((2 - (-3))^2 + (-1 - (-1))^2)
distance_AB = √(5^2 + 0^2)
distance_AB = √(25 + 0)
distance_AB = √25
distance_AB = 5 units

Next, let's find the distance from Bob's Store to Clara's house:
distance_BC = √((2 - 2)^2 + (3 - (-1))^2)
distance_BC = √(0^2 + 4^2)
distance_BC = √(0 + 16)
distance_BC = √16
distance_BC = 4 units

Now, let's find the total distance traveled if Abigail stops by Bob's Store before going to Clara's house:
distance_total = distance_AB + distance_BC
distance_total = 5 + 4
distance_total = 9 units

Therefore, if Abigail stops by Bob's Store before going to Clara's house, she will travel a distance of 9 units.

Now, let's determine the distance traveled if Abigail goes directly to Clara's house. We can use the distance formula again:
distance_AC = √((2 - (-3))^2 + (3 - (-1))^2)
distance_AC = √(5^2 + 4^2)
distance_AC = √(25 + 16)
distance_AC = √41
distance_AC ≈ 6.4 units

The difference in measurement between the two routes Abigail can take is:
differenence = distance_total - distance_AC
difference = 9 - 6.4
difference ≈ 2.6 units

Therefore, the route where Abigail stops by Bob's Store is approximately 2.6 units longer than going directly to Clara's house. The direct route to Clara's house is faster.
can you explain that now in 3 sentaces?
The distance traveled if Abigail stops by Bob's Store before going to Clara's house is 9 units. The distance traveled if Abigail goes directly to Clara's house is approximately √41 units. The direct route to Clara's house is faster than stopping by Bob's Store.