Question

1) Find AC using either the distance formula or the Pythagorean Theorem.

A) 2
B) 2/3 or 3.46
C) 2/5 or 4.47
D) 8

2) Apply the Pythagorean Theorem to find the distance between points A and B.
A) 60 units
B) 68 units
C) 9 units
D) 10 units

Answer 1

1. C) 2/5 or 4.47 if 2/5 means 2 sqrt(5)

2. sqrt(68)

Explanation:

1. using the pythagorean theorem

a^2 + b^2 = c^2

where a = distance AB = 4 b = BC = 2 and c = AC = ?

4^2 + 2^2 = c^2

16 + 4 = c^2

20 = c^2

take the square root of each side

sqrt(20) = c

sqrt(4) * sqrt(5) = c

2sqrt(5) = c

2. using the pythagorean theorem

a^2 + b^2 = c^2

where a = distance AC = 8 b = BC = 2 and c = AB = ?

8^2 + 2^2 = c^2

64 + 4 = c^2

68 = c^2

take the square root of each side

sqrt(68) = c

sqrt(4) * sqrt(17) = c

2sqrt(17) = c

did you forget to put the square root of B

Answer 2

Hi There!

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Pythagorean Thereom:
`c = √(a^2 + b^2)`

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Question 1:

a and b = both legs.

c = hypotenuse (AC)

`c = √(2^2 + 4^2)`

`c = √(4 + 16)`

`c = √(20)`

c ≈ 4.47

Answer: C) 2/5 or 4.47

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Question 2:

a and b = both legs.

c = hypotenuse (AB)

`c = √(2^2 + 8^2)`

`c = √(4 + 64)`

`c = √(68)`

c ≈ 8.25

Answer: C) 9 units

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Hope This Helps :)