Answer: Choice B) {3, 5, sqrt(34)}
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Explanation:
We can only have a right triangle if and only if a^2+b^2 = c^2 is a true equation. The 'c' is the longest side, aka hypotenuse. The legs 'a' and 'b' can be in any order you want.
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For choice A,
a = 2
b = 3
c = sqrt(10)
So,
a^2+b^2 = 2^2+3^2 = 4+9 = 13
but
c^2 = (sqrt(10))^2 = 10
which is not equal to 13 from above. Cross choice A off the list.
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Checking choice B
a = 3
b = 5
c = sqrt(34)
Square each equation
a^2 = 3^2 = 9
b^2 = 5^2 = 25
c^2 = (sqrt(34))^2 = 34
We can see that
a^2+b^2 = 9+25 = 34
which is exactly equal to c^2 above. This confirms the answer.
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Let's check choice C
a = 5, b = 8, c = 12
a^2 = 25, b^2 = 64, c^2 = 144
So,
a^2+b^2 = c^2
25+64 = 144
89 = 144
which is a false equation allowing us to cross choice C off the list.
The formula is y=mx+b
To get the slope or m, use this formula
(the second y minus the first y)/(the second x minus the first x)
Now set it up.
(10-7)/(2--1)
3/3=slope is 1.
y=1x+b
Insert one of the points for x and y.
i will do (-1,7)
7=1(-1)+b
7=-1+b
8=b
Insert this into the final equation:
y=1x+8
Try it out. If you're not sure, try both points. If it works, then you set it up correctly.
Combine like terms and "plug in" x into the equation to eventually get 34 after some addition
