Question

1) What is the distance between points R and S? Round to the nearest hundredth.

A) 9.43
B) 13
C) 10.23
D) 80


2) Which of these IS a Pythagorean triple?

A) 11,60,61
B) 6,8,15
C) 5,11,12
D)

Answer 1

1)

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have R(2, -2) and S(7, 6). Substitute:

`d=√((6-(-2))^2+(7-2)^2)=√(8^2+5^2)=√(64+25)=√(89)\\\\\boxed{d\approx9.43}`

Answer: A) 9.43

2)

If a, b and c are a Pythagorean triple, then:

`a^2+b^2=c^2`

for a ≤ b < c.

We have:

A) 11, 60, 61

check:

`11^2+60^2=121+3600=3721\\\\61^2=3721`

CORRECT

B) 6, 8, 15 - These are not the sides of the triangle because 6 + 8 = 14 < 15

C) 5, 11, 12

check

`5^2+11^2=25+121=146\\\\12^2=144\\\\146\\eq144`

INCORRECT

Answer: A) 11, 60, 61