Free Printable Pythagorean Theorem and Distance Formula

1.

What formula will correctly display how to find the distance of side r?

a)

x² + y²= r²

b)

x + y = r

c)

x - y = r

d)

x² - y²= r²

2.

If you can't remember the Pythagorean formula, what other formula you use?

a)

The Distance Formula

b)

The Midpoint Formula

c)

The Quadratic Formula

d)

The Circumference Formula

3.

A line segment has endpoints R(-8, 4) and S(5, -3). Which statement BEST explains the relationship between the length of line segment RS and the coordinates of the endpoints?

a)

RS² = (-8 - 5)² + (4 - (-3))² because RS is the hypotenuse of a right triangle with side lengths equal to the difference in x- coordinates and the difference in y-coordinates

b)

RS² = (-8 - 5)² + (4 - (-3))² because RS is equal to the sum of the differences in x coordinates and y coordinates

c)

RS = (-8 - 5)² + (4 - (-3))² because RS is equal to the sum of the differences in x coordinates and y coordinates

d)

RS = (-8 - 5)² + (4 - (-3))² because RS is the hypotenuse of a right triangle with side lengths equal to the difference in x- coordinates and the difference in y-coordinates

4.

What is the formula for finding the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

5.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

6.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

7.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

8.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

9.

An 11 meter ladder is propped up against a building 4 meters from the base of the building. How far up the building is the ladder reaching?

a)

√105

b)

15

c)

7

d)

√136

10.

What is the perimeter of the rectangle ABCD?

a)

46 cm

b)

50 cm

c)

17 cm

d)

25 cm

11.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

12.

Find the distance between (3, 24) and (7, 56).

a)

32.1

b)

32.2

c)

32.3

d)

32.4

13.

Becky leaves school to go home. She walks 6 blocks North and then 8 blocks west. How far is Becky from the school?

a)

14 blocks

b)

12 blocks

c)

10 blocks

d)

8.5 blocks

14.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

15.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

16.

Find h

a)

35.60

b)

35.00

c)

35.71

17.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

18.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

19.

Do the segment lengths 15, 12, and 9 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

20.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

21.

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)

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

22.

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

a)

3

b)

4

c)

5

d)

7

23.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

24.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

25.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

26.

Find the distance between (-3, -11) and (8, -42).

a)

32.1

b)

32.3

c)

32.7

d)

32.9

27.

Find the distance between (-5, -8) and (-1, -16).

a)

8.9

b)

9.8

c)

10.3

d)

11

28.

What is the distance between (2,9) and (1,5)?

a)

15

b)

17

c)

4.12

d)

3.87

29.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

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

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

30.

Find the distance.

a)

7.1

b)

7.8

c)

8.7

d)

8.9

31.

Granny Gardner has a rectangular vegetable garden that has a length of 6o feet. She runs a 61 foot hose diagonally across her garden. What is the width of Granny’s garden?

a)

1

b)

86

c)

11

d)

121

32.

A 24-inch television measures 24 inches diagonally and has a width of 16.8 inches. To the nearest tenth, what is the height of the TV? Round to the nearest tenth.

(a)

33.

A pool table measures 4 feet by 8 feet. What is the distance, to the nearest tenth of a foot, from one corner pocket to the opposite corner pocket? Round to the nearest tenth.

(a)

34.

a)

A

b)

B

c)

C

d)

D

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

a)

25

b)

5

c)

10

d)

35

39.

a)

127.3

b)

16200

c)

180

d)

90.8

40.

a)

9.4

b)

9

c)

13

d)

89

41.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

42.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

43.

The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 3 feet tall and 6 feet wide?

a)

18

b)

6.7

44.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

45.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

46.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

47.

Madison is on the top of an 80 foot building. She is creating a zipline course to the ground with 100 feet of cable. How far from the base of the building will she need to anchor the cable to make the zipline cable tight?

a)

60 feet

b)

20 feet

c)

180 feet

48.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

49.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

a)

65 miles

b)

89 miles

c)

45.4 miles

d)

We don't have enough information.

50.

What is the length of a diagonal of a rectangular picture whose sides are 12 inches by 17 inches? Round to the nearest tenth of an inch. DO NOT INCLUDE UNITS ON YOUR ANSWER.

(a)

51.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

52.

The Pythagorean Theorem is
c² = a² - b²

a)

false

b)

true

53.

In a right triangle __________is ALWAYS the longest side.

a)

a leg

b)

a hypotenuse

54.

Sides a and b are called legs.

a)

true

b)

false

55.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

56.

The diagram shows three squares that are joined at vertices to form a right triangle.

Which statement is true?

a)

The sum of the areas of square A and square C is equal to the area of square B.

b)

The sum of the areas of square B and square C is equal to the area of square A.

c)

The sum of the areas of square of C and Square B and square A equal to the area of square C.

d)

The sum of the areas of square A and Square B is equal to the area of square C.

57.

A teacher is showing his student Jacob to join three squares at their vertices to create the figure shown in the diagram.

The student will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

a)

The number of tiles needed to cover Square R is the same as the number of square tiles needed to cover Square G and Square M

b)

The number of tiles needed to cover Square G is the same as the number of tiles needed to cover both Square R and Square M.

c)

The number of tiles needed to cover Square M is the same as the number of square tiles needed to cover Square R and Square G.

58.

What is the distance between the two points?

a)

12.6

b)

11.8

c)

12.7

d)

12

59.

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

60.

Which side is the hypotenuse?

a)

a

b)

b

c)

c

61.

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

a)

9

b)

40

c)

41

62.

Fill in the blank: The _______ of the squares on the legs is equal to the area of the square on the hypotenuse

a)

difference

b)

square root

c)

sum

d)

product

63.

Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.

a)

No, because 10+11 does not equal 13

b)

No, because 100+121 does not equal 169

c)

Yes, because there is a small side, medium side and long side

d)

Yes, because a triangle has 3 sides

64.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

65.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

66.

1. When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

yes

b)

no

67.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

yes, because the area of the smaller square and the area of the larger square is equal to the area of the medium square.

b)

yes, because the sum of the area of smaller square and the area of the medium square is equal to the area of the larger square.

c)

No, because the difference of the area of the medium square and the area of the larger square is equal to the area of the smaller square.

d)

No, because the sum of the area of smaller square and the area of the medium square does not equal to the area of the larger square.

68.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

yes, because the sum of the area of the large square and the area of the small square is equal to the area of the medium square.

b)

Yes, because the sum of the area of the small square and the area of the medium square is equal to the area of the larger square.

c)

No, because the sum of the area of the large square and the area of the medium square is not equal to the area of the smaller square.

d)

No, because the sum of the area of the small square and the area of the medium square is not equal to the area of the larger square.

69.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

yes

b)

no

70.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

$yes,\ because\ a^2\ +\ b^2\ =c^2$

b)

$no,\ because\ a^2\ +\ b^2\ \ne c^2$

71.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square. Do these three squares support this statement?

a)

yes

b)

no

72.

1. When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square.

Which three squares do NOT support this statement?

a)

b)

c)

73.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the larger square.

Which three squares support this statement? (note 2 answers)

a)

b)

c)

d)

74.

The diagram shows three squares that are joined at vertices to form a right triangle.

Which statement is true?

a)

The sum of the areas of square A and square C is equal to the area of square B.

b)

The sum of the areas of square B and square C is equal to the area of square A.

c)

The sum of the areas of square of C and Square B and square A equal to the area of square C.

d)

The sum of the areas of square A and Square B is equal to the area of square C.

75.

A teacher is showing his student Jacob to join three squares at their vertices to create the figure shown in the diagram.

The student will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

a)

The number of tiles needed to cover Square R is the same as the number of square tiles needed to cover Square G and Square M

b)

The number of tiles needed to cover Square G is the same as the number of tiles needed to cover both Square R and Square M.

c)

The number of tiles needed to cover Square M is the same as the number of square tiles needed to cover Square R and Square G.

Pythagorean Theorem and Distance Formula

Total questions: 75

Worksheet time: 4hrs 25mins

Similar Resources on Wayground