Answer:
d(x) = √[(x - 2)² + (3x - 1)²]
Step-by-step explanation:
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, the distance between point (2,0) and a point (x,y)
d = √[(x - 2)² + (y - 0)²]
d = √[(x - 2)² + (y)²]
But the point (x,y) is on the line y = 3x - 1
We can substitute for y in the distance between points equation.
d(x) = √[(x - 2)² + (3x - 1)²]
QED!
about the second one... well, is a "fait accompli" that using the pythagorean theorem, if x = 8 and y = 5, the hypotenuse must be √(8² + 5²) = √(89), which is neither of those choices.
5, 8, 13 are no dice, namely 5² + 8² ≠ 13
25, 64, 17 is are no dice too, because 25² + 17² ≠ 64²
however, 5,12 and 13 are indeed a pythagorean triple
also is 39, 80, 89.
when looking for a pythagorean triple, recall that c² = a² + b².
so the longest leg is the sum of the square of the small ones.
so what you'd do is, check the small legs, square them, add them up, if they're indeed a pythagorean triple, they "must" add up to the longest leg.