Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Algebra What are the coordinates of the vertices of each figure?

7. rectangle with base b and height h

   

8. square with sides of length a

   

9. square centered at the origin, with side length b

   

10. parallelogram where S is a units from the origin and Z is b units from the origin

    

11. rhombus centered at the origin, with S W = 2 r s w equals 2 r  and T Z = 2 t t z equals 2 t

    

12. isosceles trapezoid with base centered at the origin, with base 2a and O R = c o r equals c

    

See Problem 2.

13. The diagram below shows a parallelogram. Without using the Distance Formula, determine whether the parallelogram is a rhombus. How do you know?

    

See Problem 3.

14. Plan a coordinate proof to show that the midpoints of the sides of an isosceles trapezoid form a rhombus.

    1. Name the coordinates of isosceles trapezoid TRAP below, with bottom base length 4a, top base length 4b, and E G = 2 c . e g equals 2 c .  The y-axis bisects the bases.

       

    2. Write the Given and Prove statements.
    3. How will you find the coordinates of the midpoints of each side?
    4. How will you determine whether DEFG is a rhombus?

B Apply

15. Open-Ended Place a general quadrilateral in the coordinate plane.
16. Reasoning A rectangle LMNP is centered at the origin with M ( r , − s ) . m open r comma negative s close .  What are the coordinates of P?

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