For part A: two transformations will be used. First we will translate ABCD down 3 units: or the notation version for all (x,y) → (x, y - 3) so our new coordinates of ABCD will be: A(-4,1) B(-2,-1) C(-2,-4) D(-4,-2)
The second transformation will be to reflect across the 'y' axis. Or, the specific notation would be: for all (x,y) → (-x, y) New coordinates for A'B'C'D' A'(4,1) B'(2,-1) C'(2,-4) D'(4,-2)
Part B: The two figures are congruent.. We can see this a couple of different ways. - first after performing the two transformations above, you will see that the original figure perfectly fits on top of the image.. exactly the same shape and size. - alternatively, you can see that the original and image are both parallelograms with the same dimensions.
