Amy, David, Euan, Lewis and Robert at St. Nicolas School, Newbury tried solving this problem. They have explained their solution very clearly although it is quite long!

The shape ABCD is a trapezium. We think the coordinates are A
(4,2) B (6,2) C(7,1) D (3,1)

After moving 3 squares left and 4 up the new coordinates are A
(1,6) B (3,6) C (4,5) D (0,5). We noticed that the x coordinate of
the new number was 3 less than the original coordinate and the y
coordinate was 4 more than the original coordinate.

We reflected the shape in the x axis. The new coordinates are
A (4,-2) B(6,-2) C (7,-1) D (3,-1). The x coordinate stayed the
same but the y coordinate has got a minus in front of it. We
predicted the new coordinates after reflecting in the y axis A
(-4,2) B (-6,2) C (-7,1) D (-3,1)

We reflected the original shape in the line y = -x. The new
coordinates we found were A (-2,-4) B (-2,-6) C (-1,-7) D (-1,-3).
These coordinates are the ones we came up with when we predicted
reflecting the 3 points in the line y = -x. (-4,-2) (4,-6)
(5,5)

When we took the original shape and rotated it anticlockwise
about the origin, we came up with these coordinates A (-2,4) B
(-2,6) C (-1,7) D (-1,3)

Looking at the patterns we found, this transformation could
also be described as reflecting in the line y = -x and then
reflecting in the x axis.

Example A starts (4,2), after reflecting in the line y = -x it
is (-2,-4), and then reflecting in the x axis it is (-2,4), which
is the same as rotating through 90 degrees.