Answer:
See explanation
Step-by-step explanation:
a) To prove that DEFG is a rhombus, it is sufficient to prove that:
- All the sides of the rhombus are congruent:
- The diagonals are perpendicular
Using the distance formula;
Using the slope formula;
The slope of EG is
The slope of EG is undefined hence it is a vertical line.
The slope of DF is
The slope of DF is zero, hence it is a horizontal line.
A horizontal line meets a vertical line at 90 degrees.
Conclusion:
Since and , DEFG is a rhombus
b) Using the slope formula:
The slope of DE is
The slope of FG is