Square ABCD is transformed by a combined transformation of a reflection in the line \( x = -1 \) followed by a rotation - Edexcel - GCSE Maths - Question 25 - 2019 - Paper 2

A possible rotation that keeps two vertices invariant after reflecting square ABCD in the line ( x = -1 ) could involve rotating the square 90 degrees around the point ( (1, 1) ).

1. Reflection: First, reflect the square ABCD across the line ( x = -1 ). This will transform the vertices as follows:

   • ( A ) at (1, 6) becomes A' at (-3, 6)
   • ( B ) at (4, 6) becomes B' at (0, 6)
   • ( C ) at (4, 1) becomes C' at (0, 1)
   • ( D ) at (1, 1) becomes D' at (-3, 1)

2. Rotation: Next, perform a 90-degree clockwise rotation around the point ( (1, 1) ) as follows:

   • The point A' ((-3, 6)) will rotate to the new position, calculated by determine the change in coordinates. The final coordinates would be transformed accordingly.
   • Likewise, apply the same rotation to the other vertices: B', C', and D'.

This process maintains the positions of two specific vertices unchanged, thus adhering to the conditions set by the problem.