1. give an example of a group, g, and a proper subgroup, h, where h has finite index in g and h has infinite order 2. give an example of a group, g, and a proper subgroup, h, where h has infinite index in g and h has finite order. (hint: you won't be able to find this with the groups that we work a lot with. try looking in so2(r))

Igure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below: 4 quadrant coordinate grid showing two parallelograms. figure 1 has vertices at negative 5, 2 and negative 3, 4 and negative 4, 7 and negative 6, 5. figure 2 has vertices at 5, negative 2 and 7, negative 4 and 6, negative 7 and 4, negative 5. which two transformations can map figure 1 onto figure 2? reflection across the y-axis, followed by reflection across x-axis reflection across the x-axis, followed by reflection across y-axis reflection across the x-axis, followed by translation 10 units right reflection across the y-axis, followed by translation 5 units down