Question

A stadium is 5 miles east and 5 miles north of the hospital. It is located at (5, 5) on the map. Is this inside, outside, or on the circle drawn by the paramedics?

Answer 1

Explanation:

Answer 2

Pythagorean Theorem states that:

`{c}^(2) = {a}^(2) + {b}^(2)`
If a = 5, and b = 5, then:

`{c}^(2) = {5}^(2) + {5}^(2)`

`so \: c = \sqrt{( {5}^(2) + {5}^(2)) } = √(50) \\ = √(25) * √(2) = 5 √(2)`
The equation of that circle, where origin is center, is:

`{x}^(2) + {y}^(2) = {r}^(2) \\ where \: r = radius \\ so \: {x}^(2) + {y}^(2) = {5}^(2) \\ {x}^(2) + {y}^(2) = 25`
That point (5, 5) lies directly on this circle.