Give the coordinates for point P without using any new variables.

17. isosceles trapezoid

    

18. trapezoid with a right ∠ angle

    

19. kite

    

20. 1. Draw a square whose diagonals of length 2b lie on the x- and y-axes.
    2. Give the coordinates of the vertices of the square.
    3. Compute the length of a side of the square.
    4. Find the slopes of two adjacent sides of the square.
    5. Writing Do the slopes show that the sides are perpendicular? Explain.
21. Make two drawings of an isosceles triangle with base length 2b and height 2c.
    1. In one drawing, place the base on the x-axis with a vertex at the origin.
    2. In the second, place the base on the x-axis with its midpoint at the origin.
    3. Find the lengths of the legs of the triangle as placed in part (a).
    4. Find the lengths of the legs of the triangle as placed in part (b).
    5. How do the results of parts (c) and (d) compare?
22. W and Z are the midpoints of O R ¯ o r bar  and S T ¯ , s t bar , comma  respectively. In parts (a)–(c), find the coordinates of W and Z.
    1. 
    2. 
    3. 
    4. You are to plan a coordinate proof involving the midpoint of W Z ¯ . w z bar , .  Which of the figures (a)–(c) would you prefer to use? Explain.

Plan the coordinate proof of each statement.

23. Think About a Plan The opposite sides of a parallelogram are congruent (Theorem 6-3).
    • How will you place the parallelogram in a coordinate plane?
    • What formulas will you need to use?
24. The diagonals of a rectangle bisect each other.
25. The consecutive sides of a square are perpendicular.

Classify each quadrilateral as precisely as possible.

26. A(b, 2c), B(4b, 3c), C(5b, c), D(2b, 0)
27. O(0, 0), P(t, 2s), Q(3t, 2s), R(4t, 0)
28. E ( a , b ) , F ( 2 a , 2 b ) , G ( 3 a , b ) , H ( 2 a , − b ) e open eh comma b close comma f open 2 eh comma 2 b close comma g open 3 eh comma b close comma h open 2 eh comma , negative b , close
29. O ( 0 , 0 ) , L ( − e , f ) , M ( f − e , f + e ) , N ( f , e ) o open 0 comma 0 close comma , l open minus , e comma f close comma m , open f minus , e comma f plus e close comma n open f comma e close

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