Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.

Question

Using the transformation T: (x, y)  (x + 2, y + 1), find the distance named.

anonymous · Answer

attachment

anonymous · Answer

please explain steps to solve

anonymous · Answer

What distance are we looking for, exactly?

anonymous · Answer

AB

anonymous · Answer

Okay, to find the distance between A and B, all we need is the Pythagorean theorem. We know that a right triangle with sides x and y will have a hypotenuse of sqrt(x^2+y^2):
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If you look at the picture you sent, the line between A and B is the hypotenuse of a right triangle with legs 1 and 3. So, the distance is sqrt(1^2+3^2) = sqrt(10).

anonymous · Answer

I'm not sure why the transformation is important, unless it's another part of the problem. It is good to know, though, that a translation (where you just shift points, by adding some constant to x and some constant to y) will preserve distances. So, in this case, the distance between A' and B' is the same as the distance between A and B.

anonymous · Answer

So, do you understand how to do it now?

anonymous · Answer

yes! it makes perfect sense! thank you

anonymous · Answer

great :)