What best describes a theorem in an axiomatic system

The coordinate grid shows a pentagon. the pentagon is translated 3 units to the right and 5 units up to create a new pentagon. what is the rule for the location of the new pentagon?

Chase is working to earn money for a cd player. on saturday, he earned half as much as he did on sunday, but twice as much as he did on friday. during the 3 days, he earned $70.00. how much did he earn each day?

The smaller triangle is a pre-image of the bigger triangle. the center of dilation is (1, −1). what is the scale factor used to create the dilation?