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Geometry Spring Term Benchmark Review: CoordinateGeo/Trig/Circle

Total questions: 82

Worksheet time: 2hrs 3mins

Name
Class
Date
1.

Which formula can be used to find the distance between 2 points on the coordinate plane?

a)
b)
c)
d)
2.

What is the perimeter of a rectangle with corners at (2,2), (2,-4), (-5,-4), and (-5,2).

a)

13 units

b)

26 units

c)

42 units

d)

10 units

3.

What is the area of a rectangle with corners at (2,2), (2,-4), (-5,-4), and (-5,2).

a)

11 units2

b)

42 units2

c)

13 units2

d)

26 units2

4.

Calculate the length for each side of the triangle.

a)

AB = 3.6, BC = 4.5, AC = 4.1

b)

AB = 4.1, BC = 5.6, AC = 7.5

c)

AB = 4.5, BC = 3.6, AC = 4.1

d)

AB = 4.1, BC = 3.6, AC = 4.5

5.

What is the perimeter of the triangle? (Round to the nearest tenth)

a)

12

b)

about 13.2

c)

21

d)

about 12.6

6.

What is the approximate perimeter of right triangle ABC? (round to the nearest whole number)

a)

17 units

b)

15 units

c)

14 units

d)

16 units

7.

Calculate the length for each side of the rectangle.

a)

AB = 9, BC = 4.5, CD = 9, DA= 4.5

b)

AB = 6, BC = 3.29, CD = 6, DA= 3.29

c)

AB = 6.31, BC = 4.1, CD = 6.31, DA= 4.1

d)

AB = 5.65, BC = 4.24, CD = 5.65, DA= 4.24

8.

Calculate the perimeter of the rectangle.

a)

27 units

b)

18.58 units

c)

14.73 units

d)

19.78 units

9.

What is the perimeter of rectangle ABCD? Round to the nearest whole number if necessary.

a)

18 units

b)

19 units

c)

12 units

d)

25 units

10.

What is the perimeter (in units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

65

b)

8.06

c)

14

d)

19.06

11.

What is the area (in units2) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

16 units2

b)

28 units2

c)

14 units2

d)

32 units2

12.

What is the perimeter of the parallelogram? Round to the nearest hundredth if necessary.

a)

20.95 units 

b)

20.94 units

c)

18.33 units 

d)

18.32 units

13.
What is the area of the rectangle?
a)
28 units squared
b)
45 units squared
c)
33 units squared
d)
19 units squared
14.
What is the area of the figure? 
a)
11 square units
b)
15 square units
c)
25 square units
d)
30 square units
15.
What is the area of the quadrilateral with vertices at (-1, 0), (2, 0), (2, 5), and (-1, 5)?
a)
15 square units
b)
12 square units
c)
10 square units
d)
5 square units
16.
What is the area of this figure?
a)
7 units2
b)
15 units2
c)
7 1/2 units2
d)
15 1/2 units2
17.

Square ABCD has vertices A(-2,-3), B(4, -1), C(2, 5), and D(-4, 3). What is the area of the square?

a)

2102\sqrt{10}

b)

4104\sqrt{10}

c)

40

d)

20

18.

Find the area of rectangle ABCD. (Hint: You'll need to use the distance formula to find the side lengths).

a)

4.47

b)

11.18

c)

30.0

d)

22.36

19.

Find the missing side.

a)

18

b)

16

c)

17

d)

19

20.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
21.

A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is the distance? Round your answer to the nearest whole number.

a)

30 meters

b)

83 meters

c)

164 meters

d)

260 meters

22.
A 10-foot ladder is leaning against the wall.  The bottom of the ladder is 4 feet from the base of the wall.  Which of the following is closest to the distance from the top of the ladder to the base of the wall?
a)
9ft
b)
11ft
c)
6ft
d)
14ft
23.
Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. What is the length of the diagonal, in yards, that Tanya runs? 
a)
26.5 yards
b)
10 yards
c)
50 yards
d)
46.7 yards
24.
a)
7 ft
b)
5 ft
c)
3 ft
d)
2 ft
25.
if a = 3 feet,  b = 8 feet,  and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?
a)
8.54 feet
b)
10.44 feet
c)
10 feet
d)
4.12 feet
26.
a)
A
b)
B
c)
C
d)
D
27.
a)
A
b)
B
c)
C
d)
D
28.
a)
A
b)
B
c)
C
d)
D
29.
Find Cos(A) as a decimal rounded the the nearest ten-thousandth.
a)
.4706
b)
1.875
c)
.8824
d)
.5333
30.

A kite is flying 84 ft off the ground, and it string is pulled taut. The angle of elevation of the kite is 65°65\degree .  Find the length of the string.  Round your answer to the nearest tenth.

a)

198.8 ft

b)

92.7 ft

c)

39.2 ft

d)

76.1 ft

31.
Find x round to the nearest tenth.
a)
46.1
b)
4.9
c)
16.4
d)
26.9
32.
Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 
a)
63 ft
b)
65 ft
c)
74 ft
d)
87 ft
33.

If a tree casts a 8-meter shadow, and the angle from the ground to the tree is 30 degrees, what is the height of the tree?

a)

2.3

b)

6.9

c)

10.3

d)

4.6

34.
Find the measure of the indicated angle (?) round to the nearest tenth.
a)
9.4
b)
55.2
c)
20.15
d)
19.4
35.
Find the measure of the missing angle.
a)
64o
b)
26o
c)
61o
d)
.008o
36.
Solve for the missing angle
a)
50
b)
0.053
c)
36.9
d)
95
37.

Jake is 6 ft. tall. He is standing outside when the angle of elevation of the sun is 28 degrees. How long would his shadow be?

a)

5.3 feet

b)

2.8 feet

c)

3.2 feet

d)

11.3 feet

38.

The vertices of triangle GHI are G(1, 2), H(3, 4), and I(4, 2). The triangle will be reflected across the x-axis. What will be the coordinates of the image point H′?

a)

(-3, 4)

b)

(3, -4)

c)

(-3, -4)

d)

(3, 4)

39.
Reflect Point C over the y-axis:
a)
(-3, 2)
b)
(3,2)
c)
(-2,3)
d)
(3,0)
40.
What is the rule for the following reflection? 
a)
Reflection across       y = 3
b)
Reflection across        x = −3
c)
Reflection across            x = 3
d)
Reflection across          y = −3
41.

Figure EFGH in the coordinate plane has vertices at (-5,2), (-5,-2), (-1,-2), and (-1,2). If the figure is translated 7 units to the right and 3 units down, what are the coordinates of the E'F'G'H'?

Plot the 4 new points.

42.
Triangle GHI is reflected across the x-axis.  What are the coordinates of I'?
a)
(-2, 6)
b)
(2, 6)
c)
(-6, -2)
d)
(6, 2)
43.
What transformation is happening?
(x, y) ----> (x + 2, y - 3) 
a)
slide up 2, left 3
b)
slide right 2, up 3
c)
slide right 2, down 3
d)
slide left 3, right 2
44.
How was B translated to B' if B' is at (4, -2)?
a)
Translated 6 units down
b)
Translated 2 units to the left and 6 units down
c)
Translated 2 units to the right and 6 units down
d)
Translated 2 units to the right
45.
Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.
a)
〈14,-13〉
b)
〈-14,13〉
c)
〈-40,-21〉
d)
〈40,-21〉
46.

Use the given translation rule to find the image of the point (4,2)

(a)  

47.

Use the given translation rule to find the

pre-image of the point (7,-5)

(a)  

48.
How is Quadrilateral EFGH translated to E'F'G'H'?
a)
6 down
b)
6 down, 1 right
c)
6 down, 3 left
d)
8 down, 1 right
49.

Pick a rule to describe the rotation

a)

90 degrees clockwise around the origin

b)

90 degrees counter clockwise around the origin

c)

180 degrees around the origin

50.

Pick a rule to describe the rotation

a)

90 degrees clockwise around the origin

b)

90 degrees counter clockwise around the origin

c)

180 degrees around the origin

51.
If you were to rotate ABCD 180° about the origin, what would the coordinates of B' be?
a)
(0, 0)
b)
(-6, -5)
c)
(-1, 3)
d)
(-6, 2)
52.

Rotation Rules (clockwise):

90o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90⁰ rotation clockwise?

a)

(1, 3)

b)

(3, 1)

c)

(3, -1)

d)

(1, -3)

53.

Give the coordinate of the point A after of rotation of 900 counterclockwise (anticlockwise) about the point (1, 3)

a)

(1, 4)

b)

(2, 1)

c)

(2, 7)

d)

(2, 3)

54.

Give the coordinate of point C after a rotation of 1800 about the point (-1, 1)

a)

(-5, 0)

b)

(-2, 5)

c)

(0, -3)

d)

(0, 3)

55.
What would the coordinates be for Q(4,1) after a translation 3 units left and 4 units down, then a reflection over the x-axis?
a)
(1, -3)
b)
(-1, -3)
c)
(1, 3)
d)
(-1, 3)
56.
A(-5, -1) L(-3, -2) T(-3, 2)
Rotate triangle ALT 180° clockwise about the origin, then reflect over the line x=1.
a)
A'' (5, 1) L''(3, 2) T''(3, -2)
b)
A'' (3, 1) L''(1, 2) T''(1, -2)
c)
A'' (5, -1)
L''(3, -2)
T''(3, 2)
d)
A'' (-3, 1)
L''(-1, 2)
T''(-1,-2)
57.
What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?
a)
a reflection followed by a rotation
b)
a reflection followed by a translation
c)
a translation followed by a rotation
d)
a translation followed by a reflection
58.

Plot A(4,1) B(5,4) C(1,2). Reflect it over the x-axis, then translate it 3 units left. What are the coordinates of A'B'C'?

a)

A' (-1, -1) B' (-2, -4) C' (2, -2)

b)

A' (4, -4) B' (5, -7) C' (1, -5)

c)

A' (-7, 1) B' (-8, 4) C' (-4, 2)

d)

A' (1, -1) B' (2, -4) C' (-2, -2)

59.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)2 + y2 = 9

b)

x2 + (y -7)2 = 9

c)

(x - 7)2 + y2 = 3

d)

x2 + (y -7)2 = 3

60.

What are the coordinates of the center and the radius of the circle with equation:

(x - 4)2 + (y - 3)2 = 25 ?

a)

Center (4,3)

Radius = 5 units

b)

Center (4,3)

Radius = 25 units

c)

Center (-4,-3)

Radius = 25 units

d)

Center (-4,-3)

Radius = 5 units

61.

What is the equation of the circle?

a)

(x+1)2 + (y +1)2 = 3

b)

(x+1)2 + (y -1)2 = 3

c)

(x+1)2 + (y +1)2 = 9

d)

(x-1)2 + (y -1)2 = 9

62.

A circle has a center of (-1, 3) and passes through the point (-5, 6). Write the equation of the circle.

a)

(x + 1)2 + (y - 3)2 = 5

b)

(x - 1)2 + (y + 3)2 = 25

c)

(x + 1)2 + (y - 3)2 = 25

d)

(x - 1)2 + (y + 3)2 = 5

63.
The endpoints of a diameter of a circle are (3,1) and (9,5).Find the equation of the circle?
a)
(x−6)2+(y−3)2=13
b)
(x−3)2+(y−6)2=132
c)
(x−5)2+(y−9)2=13
d)
(x−9)2+(y−5)2=169/4
64.

Convert the equation of the circle from standard to general.

a)

A

b)

B

c)

C

d)

D

65.

Identify the center and the radius of the circle in general form.

a)

A

b)

B

c)

C

d)

D

66.

Graph the circle given by the equation (x−6)2+(y−1)2=9\left(x-6\right)^2+\left(y-1\right)^2=9 and identify its center and radius.

a)

Center: (6, 1), Radius: 3

b)

Center: (0, 0), Radius: 9

c)

Center: (6, 1), Radius: 9

d)

Center: (1, 6), Radius: 3

67.

Graph the circle given by the equation (x−2)2+(y+3)2=36\left(x-2\right)^2+\left(y+3\right)^2=36 and identify its center and radius.

a)

Center: (2, -3), Radius: 6

b)

Center: (-2, 3), Radius: 6

c)

Center: (2, 3), Radius: 36

d)

Center: (-2, -3), Radius: 36

68.

Write the equation of the circle with center C( 4 , -8 ) and radius = 5

a)

( x - 4 )2 + ( y + 8 )2 = 25

b)

( x + 4 )2 + ( y - 8 )2 = 25

c)

( x - 4 )2 + ( y - 8 )2 = 25

d)

( x + 4 )2 + ( y - 8 )2 = 10

69.
What is the equation for this circle?
a)
(x+1)+(y+1)=9
b)
x²+y²=9
c)
x+y=9
70.

Which equation matches the circle on the graph?

a)

(x-3)2+(y-4)2=16

b)

(x-5)2+(y-2)2=20

c)

(x+3)2+(y+4)2=16

d)

(x-9)2+(y-16)2=32

71.

The point (3,3) is on a circle whose center is at (-1,3). Write the standard form of the equation of the circle.

a)

(x-3)2+(y-3)2=4

b)

(x-3)2+(y-3)2=16

c)

(x+1)2+(y-3)2=9

d)

(x+1)2+(y-3)2=16

72.

Use the information provided to write the standard form equation of the circle.

a)

A

b)

B

c)

C

d)

D

73.

Use the information provided to write the standard form equation of the circle.

a)

A

b)

B

c)

C

d)

D

74.
The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.
a)
(x - 2)2 + (y + 5)2 = 36
b)
(x - 5)2 + (y + 2)2 = 6
c)
(x + 5)2 + (y - 2)2 = 36
d)
(x + 2)2 + (y - 5)2 = 6
75.

What is the equation for the circle, if it has diameter endpoints at (3,-4) and (-5,-4)?

a)

(x+1)² + (y-4)² = 4

b)

(x+1)² + (y+4)² = 16

c)

(x-1)² + (y-4)² = 16

d)

(x+1)² + (y+4)² = 4

76.

If the endpoints of a diameter of a circle are (6, 2) and (0, 2), what is the equation of the circle?

a)

(x−3)2+(y−2)2=9\left(x-3\right)^2+\left(y-2\right)^2=9

b)

(x+3)2+(y+2)2=3\left(x+3\right)^2+\left(y+2\right)^2=3

c)

(x−6)2+(y+4)2=9\left(x-6\right)^2+\left(y+4\right)^2=9

d)

(x−6)2+(y+4)2=3\left(x-6\right)^2+\left(y+4\right)^2=3

77.

Which is the equation of a circle given endpoints of the diameter are (0,5) (2,3)

a)

(x - 1)2 + (y - 4)2 = 2

b)

(x - 1)2 + (y - 4)2 = 4

c)

(x + 1)2 + (y + 4)2 = 1

d)

(x + 1)2 + (y - 4)2 = 4

78.
Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0
a)
(x+2)2 + (y+3)2 = 49
b)
(x+2)2 + (y+3)2 = 13
c)
(x-2)2 + (y-3)2 = 49
d)
(x-2)2 + (y-3)2 = 13
79.
Determine the center and radius:
x2 + y2 - 10x + 8y -8 = 0
a)
C = (5,-4) r = 7
b)
C = (-5,4) r = 7
c)
C = (-4,5) r = 49
d)
C = (5,-4) r = 49
80.

Use the given general form to write the equation of the circle.

x2+y2+10x−26y+169=0x^2+y^2+10x-26y+169=0  

a)

(x+5)2+(y−13)2=625\left(x+5\right)^2+\left(y-13\right)^2=625  

b)

(x+5)2+(y−13)2=25\left(x+5\right)^2+\left(y-13\right)^2=25  

c)

(x+5)2+(y−13)2=9\left(x+5\right)^2+\left(y-13\right)^2=9  

d)

(x+13)2+(y−5)2=25\left(x+13\right)^2+\left(y-5\right)^2=25  

81.

Use the given general form to write the equation of the circle.

x2+y2−12x−18y+81=0x^2+y^2-12x-18y+81=0  

a)

(x+7)2+(y+11)2=1296\left(x+7\right)^2+\left(y+11\right)^2=1296  

b)

(x−8)2+(y+5)2=36\left(x-8\right)^2+\left(y+5\right)^2=36  

c)

(x−6)2+(y−9)2=36\left(x-6\right)^2+\left(y-9\right)^2=36  

d)

(x−4)2+(y+8)2=36\left(x-4\right)^2+\left(y+8\right)^2=36  

82.
Determine the equation of the circle in standard form: x2 + y2 + 6x - 12y + 20 = 0
a)
(x-3)2 + (y+6)2 = 25
b)
(x+3)2 + (y-6)2 = 25
c)
(x-3)2 + (y+6)2 = 45
d)
(x+3)2 + (y-6)2 = 5

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