Question

Decide whether the transformation T(x, y) = (2x, 1/2y) is an isometry, and give your reasons.

Answer 1

@mathmale @zepdrix @mathstudent55

Answer 2

Do you know what an isometry is?

Answer 3

It's where the distance of the image points are preserved just as the original points.

Answer 4

Yes, an isometry is a transformation that preserves the size of the original. A translation, a rotation, and a reflection are examples of isometries.

Answer 5

Look at your transformation.
What does x --> 2x do?

Answer 6

I think I figured out the answer. I chose two points: A(2,4) and B(3,6). If I did the transformation with (2x, 1/2y) I got A'(4,2) and B'(6,3). This is almost like as if you need to reflect the original points over the line y = x to get the image points. Since it's a reflection, it also preserves the distance and therefore T(x, y) = (2x, 1/2y) is an isometry.

Answer 7

Try the transformation with the figure above.