To compare the two distances, we can use the distance formula.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
If Abigail travels directly to Clara's house, the distance between her house and Clara's house would be:
d1 = √((2 - (-3))^2 + (3 - (-1))^2)
= √(5^2 + 4^2)
= √(25 + 16)
= √41
If Abigail stops by Bob's Store before going to Clara's house, she would have to travel from her house to Bob's Store and then from Bob's Store to Clara's house. The total distance would be the sum of the distance from her house to Bob's Store and the distance from Bob's Store to Clara's house.
The distance from her house to Bob's Store would be:
d2a = √((2 - (-3))^2 + (-1 - (-1))^2)
= √(5^2 + 0^2)
= √(25 + 0)
= 5
The distance from Bob's Store to Clara's house would be:
d2b = √((2 - 2)^2 + (3 - (-1))^2)
= √(0^2 + 4^2)
= √(0 + 16)
= 4
Therefore, the total distance if Abigail stops by Bob's Store would be:
d2 = d2a + d2b
= 5 + 4
= 9
Comparing the two distances, we see that √41 (approximately 6.4) is smaller than 9. Therefore, the direct distance to Clara's house is shorter than the distance if Abigail stops by Bob's Store.
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
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