Question

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 traveling to Clara's house. Abigail wants to compare the two distances of her choices.

How long is the distance traveled if Abigail stops by bobs store before going to Clara's house?

Determine the distance traveled if Abigail goes directly to Clara's house. What is the difference in measurement between the two routes, and which one is faster?

Answer 1

To find the distance traveled if Abigail stops by Bob's store before going to Clara's house, we can use the distance formula.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's denote Abigail's house as A (-3, -1), Bob's store as B (2, -1), and Clara's house as C (2, 3).

To find the distance from A to B, we use the formula:
d_AB = sqrt((2 - (-3))^2 + (-1 - (-1))^2)
= sqrt(5^2 + 0^2)
= sqrt(25)
= 5

To find the distance from B to C, we use the formula:
d_BC = sqrt((2 - 2)^2 + (3 - (-1))^2)
= sqrt(0^2 + 4^2)
= sqrt(16)
= 4

Therefore, the distance traveled if Abigail stops by Bob's store before going to Clara's house is d_AB + d_BC = 5 + 4 = 9 units.

To find the distance traveled if Abigail goes directly to Clara's house, we use the formula:
d_AC = sqrt((2 - (-3))^2 + (3 - (-1))^2)
= sqrt(5^2 + 4^2)
= sqrt(25 + 16)
= sqrt(41)

Therefore, the distance traveled if Abigail goes directly to Clara's house is sqrt(41) units.

The difference in measurement between the two routes is sqrt(41) - 9 units.
To determine which one is faster, we compare the distances. Since sqrt(41) < 9, it means that going directly to Clara's house is faster than stopping by Bob's store before going to Clara's house.