Math 460
Test 2 Solutions
1. Find the matrix representing reflection in the line y = 2x .
Let be the angle through which the x axis must be rotated to give the line y = 2x . Then
1
cos() = 5 , sin() =
2
5
. Therefore
1
4
3
= ,
5 5 5
4
2
1
= .
sin(2) = 2 s

Math 460
Solutions to Homework 1
1. Using the axioms for a metric space, prove that an isometry of a metric space X is injective
(i.e. it is a 11 function). Find an example of a metric space X and an isometry of X that is
not surjective (i.e. it is not on

Math 460
Homework 3 Solutions
1. Let C1 be the circle of radius 1 centered at (0 , 1) , and let C2 be the circle of radius 2
centered at (0 , 5) . Let 1 , 2 be inversions in C1 , C2 respectively. Express each of 1 , 2 , 1
2 as a fractional linear transfo