But…. I don’t suppose a qualification “using the Manhattan distance, we obtain” would have earned this student more points.

@Barry: you beat me to the punch. But the student still got it wrong for the first question if s/he used Taxicab Geometry. That answer should be 4.

@Michael. Although the student is wrong, you are wrong too. according to my calculation, the answer should be 5.
distance= sqrt( (4-1)^2 + (5-1)^2 ) = sqrt(9+16) = 5

@HarperdeFermat:disqus : it seems like you didn’t read the previous posts carefully enough: the question was whether this student was thinking about Taxicab geometry in which case the answers should have been 4, 7, 12, and 136. So if that was their thinking, then they should have had the answer of 4 for the first question.

Of course the teacher was expecting Pythagorean distances, not Taxicab distances.

Is it possible in part a that, since the points are so close visually, the student just took two ‘diagonal’ steps first from (-1, -1) to the origin and then from the origin to (1, 1)?

This does seem like it should work, doesn’t it? It takes a while for students to get out of that nasty little habit. (I was one of those students, myself!)

Maybe the student is mixing formulas for slope and distance too?

## 7 replies on “The distance between (1,1) and (4,5) is 7”

In Taxicab geometry, this is correct!

http://en.wikipedia.org/wiki/Taxicab_geometry

But…. I don’t suppose a qualification “using the Manhattan distance, we obtain” would have earned this student more points.

@Barry: you beat me to the punch. But the student still got it wrong for the first question if s/he used Taxicab Geometry. That answer should be 4.

@Michael. Although the student is wrong, you are wrong too. according to my calculation, the answer should be 5.

distance= sqrt( (4-1)^2 + (5-1)^2 ) = sqrt(9+16) = 5

@HarperdeFermat:disqus : it seems like you didn’t read the previous posts carefully enough: the question was whether this student was thinking about Taxicab geometry in which case the answers should have been 4, 7, 12, and 136. So if that was their thinking, then they should have had the answer of 4 for the first question.

Of course the teacher was expecting Pythagorean distances, not Taxicab distances.

Is it possible in part a that, since the points are so close visually, the student just took two ‘diagonal’ steps first from (-1, -1) to the origin and then from the origin to (1, 1)?

This does seem like it should work, doesn’t it? It takes a while for students to get out of that nasty little habit. (I was one of those students, myself!)

Maybe the student is mixing formulas for slope and distance too?