30. What property of a rhombus makes it convenient to place its diagonals on the x- and y-axes?
31. Marine Archaeology Marine archaeologists sometimes use a coordinate system on the ocean floor. They record the coordinates of points where artifacts are found. Assume that each diver searches a square area and can go no farther than b units from the starting point. Draw a model for the region one diver can search. Assign coordinates to the vertices without using any new variables.

C Challenge

Here are coordinates for eight points in the coordinate plane ( q > p > 0 ) . open q greater than . p greater than 0 close .  A (0, 0), B (p, 0), C(q, 0), D ( p + q , 0 ) , d , open p plus , q comma 0 close comma  E(0, q), F(p, q), G(q, q), H ( p + q , q ) . h , open p plus , q comma q close .  Which four points, if any, are the vertices for each type of figure?

32. parallelogram
33. rhombus
34. rectangle
35. square
36. trapezoid
37. isosceles trapezoid

Standardized Test Prep

SAT/ACT

38. Which number of right angles is NOT possible for a quadrilateral to have?
    1. exactly one
    2. exactly two
    3. exactly three
    4. exactly four
39. The vertices of a rhombus are located at (a, 0), (0, b), ( − a , 0 ) , open negative eh comma 0 close comma  and ( 0 , − b ) , open 0 comma negative b close comma  where a > 0 eh greater than 0  and b > 0 . b greater than 0 .  What is the midpoint of the side that is in Quadrant II?
    6. ( a 2 , b 2 ) open , eh over 2 , comma , b over 2 , close
    7. ( − a 2 , b 2 ) open negative , eh over 2 , comma , b over 2 , close
    8. ( − a 2 , − b 2 ) open negative , eh over 2 , comma negative , b over 2 , close
    9. ( a 2 , − b 2 ) open , eh over 2 , comma negative , b over 2 , close
40. In ▱ white parallelogram PQRS , PQ = 35  cm  and Q R = 12  cm. q r equals 12 , cm.  What is the perimeter of ▱ white parallelogram PQRS ?
    1. 23 cm
    2. 47 cm
    3. 94 cm
    4. 420 cm

Short Response

41. In Δ PQR , PQ > P R > QR. cap delta  One angle measures 170. List all possible whole number values for m ∠ P . m angle p .

Mixed Review

See Lesson 6-7.

42. Let X ( − 2 , 3 ) , x open negative 2 comma 3 close comma  Y(5, 5), and Z(4, 10). Is Δ XYZ cap delta  a right triangle? Explain.

See Lesson 2-2.

Write (a) the inverse and (b) the contrapositive of each statement.

43. If x = 51 , x equals 51 comma  then 2 x = 102 . 2 x equals 102 .
44. If a = 5 , eh equals 5 comma  then a 2 = 25 . eh squared . equals 25 .
45. If b < − 4 , b less than . negative 4 comma  then b is negative.
46. If c > 0 , c greater than 0 comma  then c is positive.
47. If the sum of the interior angle measures of a polygon is not 360, then the polygon is not a quadrilateral.

Get Ready! To prepare for Lesson 6-9, do Exercises 48 and 49.

See Lesson 3-7.

48. Find the equation for the line that contains the origin and (4, 5).
49. Find the equation for the line that contains (p, q) and has slope a b . eh over b , .

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