Solution to Exercise 3.35.
That student is taught the best who is told the least.
—R. L. Moore (1882–1974)

Exercise 3.35. Find an affine transformation of the Euclidean plane that is not an isometry. 

One possible example: Let

.

Let P(0, 1, 1) and Q(1, 0, 1) be points in the Euclidean plane. Then the images of P and Q are

 and  

The distances between the points are

 and  

Since d(P,Q) does not equal d(P',Q'), the matrix A is not the matrix of an isometry.