Free Printable distance formula

1.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

2.

A(3,1) B(-2,-1) written correctly is:

a)

$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$

b)

$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$

c)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

d)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

3.

Find the distance between the points (4, 3) and (0, 6).

a)

3

b)

4

c)

5

d)

7

4.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

5.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

6.

Which of the following represents the Distance Formula?

a)

$a^2\ +\ b^2\ =\ c^2$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }-\ y_1\right)^2}$

7.

Which of the following shows the correct way to insert the following coordinates into the DIstance Formula?

(3, 4) , (7, 1)

a)

$d\ =\ \sqrt{\left(4\ -\ 3\right)^2\ +\ \left(7\ -\ 1\right)2}$

b)

$d\ =\ \sqrt{\left(7\ -\ 3\right)^2\ +\ \left(1\ -\ 4\right)^2}$

c)

$d\ =\ \sqrt{\left(7\ -\ 4\right)^2\ +\ \left(1\ -\ 3\right)^2}$

d)

$d\ =\ \sqrt{\left(3\ -\ 7\right)^2\ +\ \left(4\ -\ 1\right)^2}$

e)

$d\ =\ \sqrt{\left(3\ +\ 7\right)^2\ -\ \left(4\ +\ 1\right)^2}$

8.

Find the distance between the points (5, 7) and (-2, -2).

a)

5.7

b)

5.8

c)

8.6

d)

11.4

9.

What is the distance between (-3, 2) and (5, -1)

a)

11

b)

8.5

c)

1.7

d)

7.3

10.

Find the distance between (0, 10) and (12, 1).

a)

12

b)

11

c)

15

d)

16

11.

One end of a cable is attached to the top of a flag pole and the other end is attached 6 feet away from the base of the pole. The height of the flagpole is 12 feet. What is length of the cable?

a)

13.4 ft

b)

13.1 ft

c)

6 ft

d)

10.4 ft

12.

Rectangle JKLM is shown. To the nearest tenth, what is the distance from J to L?

a)

5.0 cm

b)

10.2 cm

c)

15.3 cm

d)

21.0 cm

13.

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

a)

Right

b)

Acute

c)

Obtuse

14.

Is a triangle with sides 21, 24 and 28 right, acute or obtuse?

a)

Right

b)

Acute

c)

Obtuse

15.

Is a triangle with sides 7, 24, and 25 right, acute, or obtuse?

a)

Right

b)

Acute

c)

Obtuse

16.

To the nearest tenth, find the hypotenuse of a right triangle with legs 12.1 and 16.2.

a)

408.9

b)

116.0

c)

20.2

d)

10.8

17.

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

a)

Right

b)

Acute

c)

Obtuse

18.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

19.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

20.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

21.

On the coordinate plane, which line is the y-axis?

a)

Horizontal Line (Side to Side)

b)

Vertical Line (Up and Down)

22.

What letter is at (7, -6)?

a)

D

b)

L

c)

X

d)

There is no letter at those coordinates.

23.

What is the value of x in the right triangle shown?

a)

16cm

b)

18cm

c)

24cm

d)

√674cm

24.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

25.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

26.

Find the diameter of the circle.

a)

5 units

b)

4 units

c)

12.2 units

d)

7.5 units

27.

Find the length of the side CD.

a)

9 units

b)

√34

c)

√5

d)

3 units

28.

Find the length of the side WV.

a)

2.38 units

b)

2.73 units

c)

√2 units

d)

2.83 units

29.

The __ - axis is vertical in the coordinate plane.

a)

X

b)

Y

c)

Z

d)

None of the above

30.

How many quadrants are in a coordinate plane?

a)

1

b)

2

c)

3

d)

4

31.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

32.

What is the ordered pair for point A?

a)

( 2, 0)

b)

( 0 , 2)

c)

(0, -2)

d)

(-2,0)

33.

What is the ordered pair for point T?

a)

(3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(- 3, 3)

34.

The coordinates for the origin in the coordinate plane are________?

a)

(1,1)

b)

(0,0)

c)

(0,1)

d)

(1,0)

35.

what shape does this make

a)

rectangle

b)

parallegram

c)

trapizoid

d)

square

36.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

37.

The Pythagorean Theorem is
a² + b²+ c²

a)

false

b)

true

38.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

39.

What letter represents the hypotenuse?

a)

a

b)

b

c)

a and b

d)

c

40.

Hypotenuse

a)

Vertical side in a right triangle

b)

Longest side in a right triangle

c)

Horizontal side in a right triangle

d)

a²+ b²= c²

41.

Which choice represents the legs?

a)

a and b

b)

a

c)

b

d)

c

42.

The Pythagorean Theorem is

a² - b² = c²

a)

false

b)

true

43.

Simplify

(x ² y ⁻¹) ²

44.

Verbally explain how to simplify the problem below.

(4a³)²

4 lines

45.

Type a written response on how to simplify the problem below

$\frac{3m^{-4}}{m^3}$

4 lines

46.

Which operation would you do first in the following equation?
10 - 4 ÷ 1 · 5

a)

Subtraction

b)

Division

c)

Multiplication

d)

Addition

47.

Which operation would you do first?
( 12 + 10) ÷ 10 · 14 - 6

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

48.

Evaluate the equation:
(10+5) -6

a)

9

b)

10

c)

11

d)

12

49.

Evaluate the equation:
5 · 2 - (11 - 7)

a)

10

b)

4

c)

6

d)

11

50.

1 + 5 · 6

a)

36

b)

31

c)

35

d)

34

51.

Which operation would you do first?
2 · (15 - 2) ÷ 5

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

52.

a)

60

b)

72

c)

216

d)

432

53.

a)

48

b)

56

c)

68

d)

1250

54.

Determine whether each pair of ratios forms a proportion

a)

Proportion

b)

Not a Proportion

55.

$a^{10}\times a^4$

(a)

56.

$\frac{g^{19}}{g^{12}}$

(a)

57.

$\left(b^7\right)^2$

(a)

58.

$\frac{d^{-3}\times d^2}{\left(d^2\right)^3}$

a)

$d^7$

b)

$d^5$

c)

$\frac{1}{d^7}$

d)

$d^{ }$

59.

$\frac{m^{22}}{m^{29}}\times m^6$

a)

$m^{13}$

b)

$\frac{1}{m}$

c)

$m$

d)

$\frac{1}{m^{13}}$

60.

$\left(x^6y^3\right)^5$

a)

$x^{11}y^8$

b)

$xy^{19}$

c)

$x^{-11}y^{-8}$

d)

$x^{30}y^{15}$

61.

a)

A

b)

B

c)

C

d)

D

62.

Match the following

a)

A

1.

True

b)

B

2.

False

c)

None

3.

None

63.

(a)

64.

(a)

65.

a)

A

b)

B

c)

C

d)

D

66.

a)

A

b)

B

c)

C

d)

D

67.

a)

$1.8\times10^2$

b)

$1.8\times10^8$

c)

180,000,000

d)

180

68.

a)

1,584,000,000

b)

$1.584\times10^9$

c)

$1.584\times10^{10}$

d)

15,840,000,000

69.

a)

$2\times10^8$

b)

$2\times10^{14}$

c)

200,000,000,000,000

d)

200,000,000

70.

Which square root is between 5 and 6?

a)

$\sqrt{30}$

b)

$\sqrt{2}$

c)

$\sqrt{56}$

d)

$\sqrt{37}$

71.

\sqrt{52}

is between which two perfect squares? Choose two numbers.

a)

7

b)

8

c)

9

d)

10

72.

Which square root is between 8 and 9?

a)

$\sqrt{64}$

b)

$\sqrt{70}$

c)

$\sqrt{99}$

d)

$\sqrt{6}$

73.

What is the perimeter of this square?

a)

3 units

b)

6 units

c)

9 units

d)

12 units

74.

What's the perimeter of this triangle?

a)

10 cm

b)

11 cm

c)

12 cm

d)

13 cm

75.

What's the perimeter of this triangle?

a)

18 inches

b)

18 feet

c)

18 cm

76.

What is the perimeter of this pentagon?

a)

15 units

b)

12 units

c)

9 units

d)

6 units

77.

What is the perimeter of this shape?

a)

11 inches

b)

22inches

78.

What's the perimeter of this rectangle?

a)

26 cm

b)

27 cm

c)

28 cm

79.

What is the perimeter of the figure?

(a)

80.

What is the area of this triangle?

a)

12 sq. cm.

b)

6 sq. cm.

c)

12 cm

d)

6 cm

81.

Find the area of the rectangle.

a)

140 cm²

b)

70 cm²

c)

34 cm²

d)

64 cm²

82.

Find the perimeter of this triangle.

a)

20 cm

b)

21 cm

c)

40 cm

d)

12.5 cm

83.

What is the volume of this prism?

a)

18 cubic cm

b)

6 cubic cm

c)

9 cubic cm

84.

What is the volume of this prism?

a)

6 cubic in

b)

12 cubic in

c)

24 cubic in

85.

Bob has a rectangular prism gift box what it the volume of Bob's gift box?

distance formula

Total questions: 85

Worksheet time: 7hrs 33mins

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