Question
wo students are using the distance formula to determine the distance between (9, 4) and (–3, 8) on a coordinate grid. Their work is shown below.
Karlin’s Work
d = StartRoot (9 minus (negative 3)) squared + (4 minus 8) squared EndRoot. D = StartRoot (12) squared + (negative 4) squared EndRoot. D = StartRoot 144 + 16 EndRoot. D = StartRoot 160 EndRoot.
Abby’s Work
d = StartRoot (negative 3 minus 9) squared + (8 minus 4) squared EndRoot. D = StartRoot (negative 12) squared + (4) squared EndRoot. D = StartRoot 144 + 16 EndRoot. D = StartRoot 160 EndRoot.
Which best explains why the order in which the subtraction occurred did not cause a difference in the answers determined by the two girls?
The differences are each squared.
The differences are added together.
The square root of the differences is taken.
The differences are the same regardless of order.
Karlin’s Work
d = StartRoot (9 minus (negative 3)) squared + (4 minus 8) squared EndRoot. D = StartRoot (12) squared + (negative 4) squared EndRoot. D = StartRoot 144 + 16 EndRoot. D = StartRoot 160 EndRoot.
Abby’s Work
d = StartRoot (negative 3 minus 9) squared + (8 minus 4) squared EndRoot. D = StartRoot (negative 12) squared + (4) squared EndRoot. D = StartRoot 144 + 16 EndRoot. D = StartRoot 160 EndRoot.
Which best explains why the order in which the subtraction occurred did not cause a difference in the answers determined by the two girls?
The differences are each squared.
The differences are added together.
The square root of the differences is taken.
The differences are the same regardless of order.
Answers
GPT-4o mini
The best explanation for why the order in which the subtraction occurred did not cause a difference in the answers determined by Karlin and Abby is:
**The differences are the same regardless of order.**
This is because subtraction is commutative when calculating distances in the context of the distance formula. In both cases, they are finding the absolute differences between the coordinates, and squaring these differences means the order of subtraction does not affect the final result.
**The differences are the same regardless of order.**
This is because subtraction is commutative when calculating distances in the context of the distance formula. In both cases, they are finding the absolute differences between the coordinates, and squaring these differences means the order of subtraction does not affect the final result.