Combined Transformations... unsolvable question?

Transformation A is a reflection in the line x = 2
Transformation A followed by B is a 90 degree rotation about the point (2,4)

Fully describe transformation B.

Ok so, I made a triangle with vertices A(1,0), B(3,0) and C(2,1) and reflected it in the line x = 2 giving me A(1,4), B(3,4) and C(2,3)

I also rotated the triangle with vertices A(1,0), B(3,0) and C(2,1) by 90 degrees around (2,4) giving me A(6,3), B(6,5) and C(5,4)

Now, I need to find the transformation that turns my reflected triangle into my rotated one. It can't be rotation or translation because the sides won't match up, so I assume reflection.

The midpoints for my reflected and rotated triangle are: A(3,5,3.5), B(4.5,4.5), C(3.5,3.5). However, the line of reflection being y = x doesn't make sense... I'm wondering if the question is broken.

The edexcel answer book says the answer is "x+y=6" which it is not..

I tried the same thing with another triangle with vertices A(1,3), B(3,3), C(2,4) and I end up with the same reflection answer y=x, which doesn't make sense when you look at it graphically.

(edited 12 years ago)

Reply 1

Spungo

I think your first reflection may be in the line y = 2 instead of x = 2.
x = 2 is a vertical line and a reflection in it should map A(1,0) to (3,0), not (1,4).