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Unit 3B –Quadrilaterals and coordinate geometry review
Name _______________
Multiple Choice. Choose the best answer.
1. What is the distance between (3, 2) and (4, 7) ?
a) 5
c)
26
74
b) 82
d)
2. The vertices of a right triangle are (5, 2) , (0, 6) and (0, 2) . What is the length of the
hypotenuse?
a) 8
b) 4
c)
89
d)
41
3. Find the midpoint of a segment with endpoints A( 8,1) and B(2, 3) .
a) (3, 1)
c) (5, 2)
b) ( 5, 2)
d) (5, 2)
4. Use the diagram to find the length of MP . M is the midpoint of PQ .
a) 25
b) 50
c) 40
d) 30
5. Find the coordinates of the other endpoint of a segment with an endpoint of X (2,3)
and a midpoint M (1, 3) .
a)
b)
4,9
 4,9
c) (4,8)
d) (-5,8)
6. Use points A(5,1) , B (5, 6) , C (1, 4) and D (4, 2) to determine which of the following is
true.
a) AB  BC
c) AB  BD
b) AB  CD
d) AC  AB
7. Three coordinate points of a parallelogram are (2,1) , (4, 4) and (7, 4) . Find the fourth
vertex.
a)
b)
c)
d)
(5,1)
(2, 7)
(5, 4)
(5, 7)
8. What special type of quadrilateral has the vertices A( 2,1) , B(2, 3) , C (2,1) , and
D(2, 3) ?
a)
b)
c)
d)
Rhombus
Square
Rectangle
Parallelogram
9. The distance between two points is 10, and the
points are (5,1) and ( x, 7) . Which value could be x?
a) 11
b) 13
c)-1
d)-5
10. Which of the following points is the greatest distance from the origin?
a) (1, 4)
c)(2,4)
b) (2,3)
d)(5,1)
11. If points A and B and the origin are vertices of a triangle, what is the perimeter of
the triangle?
a) 12
c)22
b) 15
d)25
12. Find LP
a. LP = 4
b. LP = 5
c. LP = 10
d. LP =
8 6
13. Opposite angles of a parallelogram are
_________________.
a. Sometimes congruent
b. Always congruent
c. Complementary
d. Supplementary
14. Given square MNOP. The perimeter of MNOP is 72cm, NO = 2x + 6. Find x.
a. x = 15
c. x=9
b. x = 12
d. x=6
15 . Given the diagram below, find mE.
a. mE = 130
b. mE = 65
c. mE = 50
d. mE = 115
Free Response. Answer completely.
16. Use the information in the diagram to solve for x. Show your work.
17.Find the distance between the points given.
a) (1, -2) and (4, 3)
b) (-1, 4) and (5, 2)
18.Find the midpoint between the points given.
a) (8, -1) and (4, 5)
b) (-2, 5) and (4, 2)
19. What is the measure of EACH interior and exterior angle of a regular convex decagon?
20. Given the following angles measurements for a polygon, find the number of sides.
a) Each exterior angle of a regular polygon is 60°.
b) The sum of the interior angles of a polygon is 1260°.
21.
22.
Find the sum of the measures of the interior angles of a 34-gon.
Find the measure of each interior angle of a regular dodecagon.
23.
If each interior angle of a regular polygon measures 168°,
find the number of sides of the polygon. Set up an equation and solve!
24.
A pentagon has exterior angles measuring 60, 40, 70, and 53 .
What is the measure of the remaining exterior angle
25. What is the measure of each interior and exterior angle of a regular convex hexagon?
26. Find the value of each variable in the following parallelogram.
(x + 30)o
25
72o
8y + 1
27. Find x using the given information for the quadrilaterals.
B
a)
22
C
S
b) Kite
7
M
A
x
28
V
N
T
5
12
D
x
U
28. An amusement park designer wants to place a Ferris wheel midway between the two
largest coasters. The distance between consecutive grid lines is 500 feet.
a) Determine the coordinates of
where the Ferris wheel should be.
b) How far will the Ferris wheel be
from each of the coasters?
29. Use the distance formula to
determine if the quadrilateral is a
parallelogram.
30. Find x and y for the rhombus.
2x - 4
(3y)°
60°
20
31. Find x using the information given for the trapezoid.
a)
20
b)
120o
x
3xo
30
2x+5
c)
3x-8
x-7
32. The front view of a camping tent is shown below. Find the value of x. Then, determine
the measure of each angle.
(9x-14)o
(9x+1)o
10xo
5xo
(9x+1)o
10xo
5xo
33.
Find the value of each variable.
Parallelogram:
(2x + 10)o
z
30
80o
7y - 5
20
Rhombus:
6y - 5
1270
3y + 7
(2x-1)0
34. Decide if there is enough information given to determine if the figure is a parallelogram.
If so explain why.
a)
b)
c)
d)