1)
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have R(2, -2) and S(7, 6). Substitute:
[tex]d=\sqrt{(6-(-2))^2+(7-2)^2}=\sqrt{8^2+5^2}=\sqrt{64+25}=\sqrt{89}\\\\\boxed{d\approx9.43}[/tex]
Answer: A) 9.43
2)
If a, b and c are a Pythagorean triple, then:
[tex]a^2+b^2=c^2[/tex]
for a ≤ b < c.
We have:
A) 11, 60, 61
check:
[tex]11^2+60^2=121+3600=3721\\\\61^2=3721[/tex]
CORRECT
B) 6, 8, 15 - These are not the sides of the triangle because 6 + 8 = 14 < 15
C) 5, 11, 12
check
[tex]5^2+11^2=25+121=146\\\\12^2=144\\\\146\neq144[/tex]
INCORRECT
Answer: A) 11, 60, 61
