2 Geometry 1. (a) [2 marks] Let A(1 -i), B(3 + 30). Find the point C(x + iy) such that triangle ABC has side-length AC =5 AB and ZBAC is Ix clockwise. (b) [3 marks] Let A(1), B(-1+ 3(), C(2 +1), D(5 -21), E(a + bi). F(2 + 7i) be points in the complex plane. Find reals numbers a and 6 so that triangle ABC is similar to triangle DEF with A corresponding to D, B corresponding to E, and C corresponding to F. 2. (a) [2 marks] Find the equation of the isometry R which is the rotation around the point (1 + i) by an angle an anticlockwise. (b) [3 marks] Let m be the line passing through the points 1 + i and 3 + 5i. Find the equation of the isometry T' which is the reflection across the line m. (c) [2 marks] Find the equation of the isometry ( which is the translation along the line m in part (b) by a length 3 (in the direction of increasing x), then reflecting across the line m. (d) [3 marks] Let f(2) = -12 + 1 -i. Show that this is a glide reflection which is the composition of a translation U along a line m, and a reflection across m. Determine the translation U and the line m