Final answer:
The original conditional statement refers to doubling a rectangle's dimensions causing the area to increase by a factor of four. The inverse or contrapositive of this statement would respectively state the negations of the original conditions and conclusions. In geometry, the area increases by the square of the scale factor for proportional dimension changes.
Step-by-step explanation:
The student is inquiring about the effects of doubling the dimensions of a rectangle on its area, and the relationship between this scenario and certain logical conditional statements. The conditional statement in mathematical terms would be 'If the dimensions of a rectangle are doubled, then the area increases by a factor of four.' If we let p represent the original conditional statement, then -p does not represent the inverse of the original statement.
Instead, the inverse would be 'If the dimensions of a rectangle are not doubled, then the area does not increase by a factor of four.' Furthermore, q would also be an incorrect representation of the original statement, and -q would not be the contrapositive. The contrapositive should correctly state 'If the area does not increase by a factor of four, then the dimensions of the rectangle are not doubled.' When applying these principles to geometric figures, we find that the area of a geometric shape like a rectangle or square increases by the square of the scale factor when the dimensions are increased proportionally.