Question

Use the distance formula to show that T(x,y) = (-y,x) is an isometry.

Answer 1

@Nnesha @zepdrix @SolomonZelman

Answer 2

@Loser66

Answer 3

What is an isometry?

Answer 4

The distance from the two original points must be the same as the distance from the image points, for any two original points and image points.

Answer 5

Ok,
1) Let \((x_1,y_1),(x_2,y_2)\) are the original points. The distance between them is ??

Answer 6

\[\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}\]

Answer 7

2) Their images are \((-y_1,x_1), (-y_2,x_2) \) right?
The distance between them is ???

Answer 8

\[\sqrt{(-y_2 + y_1)^2 + (x_2 - x_1)^2}\]

Answer 9

Yes. Can you see they are equal?

Answer 10

No??

Answer 11

Yeah I see it with the y-coordinates.

Answer 12

dat sit.

Answer 13

Thanks! Can you help me with another question please?

Answer 14

Not sure, just post

Answer 15

Alright