There are 8 problems. On your paper, please label your work with the problem numbers 1., 2., 3., etc. below, and keep them in the same order. 1. Prove that a translation 74 g is an isometry. (Use the definitions of translation and of isometry). 2. Prove that a halfturn op is an isometry. 3. Exercise 4.3. Please write out the chart, filling in the missing entries. 4. Prove: if isometry interchanges distinct points P and @, then fixes the midpoint of P and Q. 5. Prove: reflection o, fixes every line [ that is perpendicular to m. 6. Exercise 4.7: What are the images of (0,0), (1, 3),(2,1), and (2,4) under the reflection in the line with equation = 2X 57 7. List at least five geometric properties that are preserved by an isometry. (no proofs needed) 8. Give an example of a collineation that is not an isometry. 4.3. Fill in the missing entry in each row: Equation of line m Point P Point om(P) X = 0 (x, y) Y = 0 (x, y) Y = X * (2, 3) Y = X (x, y) X = 2 (-2, 3) * Y = -3 (-4, -1) Y = -3 (x, y) (5, 3) (-8, 3) * (0, 3) (- 3, 0) * (- y, - x) (x, V) Y = 2X * (4, 3)