MT1100 Problem Sheet 2 Due: Thursday 15th October 2020 at 10:00. Please write your name clearly at the top of each page. Scan your work as a single-file PDF. Do not use too high a resolution to ensure the file size remains below 20 MB (the upper limit is 50MB). Then upload your PDF file onto Moodle, as per the instructions available from the General Information box on Moodle. You are encouraged to leave your handwritten comments to the marker on the first or last page of your homework submission. This sheet asks you for some ruler and compass constructions. Remember the structure: diagram, list of steps (basic ones or previous constructions), justification. 1. Suppose we are given points A and B such that |AB| = 1. Construct, using a ruler and compass, a point Y such that |AY| = 3. [I'm asking for a diagram, a list of steps in the construction, and a justification. This shows that 3 is a constructible length.] 2. Given three points X, Y and Z that are not all in a line, construct (using a ruler and compass) the circle C that passes through these three points. [I'm asking for a diagram, a list of steps in the construction, and a justification. Hint: The plenary lecture showed how to construct a perpendicular bisector!]