I presume you are doing a positive rotation which is anticlockwise. You can measure 45 degrees with a pertractor and then draw a faint line. Then a compass can be used to find the new coordinates.
The question:
Show that the order in which transformations is important by first sketching the result when the triangle A(1,0) B(1,1) C(0,1) is rotated by 45 degrees about the origin and then translated by (1,0), and then sketch the result when it is first translated then rotated.
I'm not sure how to determine its position after rotation. Do I have to use a transformation matrix? If so, how would I apply it to this question? Thanks.
Well, we can't say what your teacher wants!
A rotation about the origin of degrees corresponds to a matrix multiplication with matrix . That is the same as saying ,
Here, so ,
That is, (1, 0) is mapped into , (1, 1) is mapped into and (0, 1) is mapped into .
You should be able to see how that matches your graph. Now, "translate by (1, 0)" by adding 1 to each x coordinate.
It should be easy to see why moving the object away from the origin before rotating is different from rotating and then moving the object.