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

Pythagorean Theorem states that:
${c}^{2} = {a}^{2} + {b}^{2}$
If a = 5, and b = 5, then:
${c}^{2} = {5}^{2} + {5}^{2}$
$so \: c = \sqrt{( {5}^{2} + {5}^{2}) } = \sqrt{50} \\ = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}$
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.