Question

Does the point (–3, 2) lie inside, outside, or on a circle with center (4, 0) and radius 5 units?

Answer 1

Answer:

The point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.

Step-by-step explanation:

The distance between two points (x₁, y₁) and (x₂, y₂) on the x-y plane can be calculated with:

√((x₁ - x₂)² + (y₁ - y₂)²)

So in this case, with the points (-3, 2) and (4, 0), the distance is:

√((-3 - 4)² + (2 - 0)²)

√(49 + 4)

√(53) ≈ 7.28

Since 7.28 > 5, the point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.