Question

Distance between two points in the plane: Decimal answers

Calculate the distance between the points A = (3, 0) and F=(-2, -3) in the coordinate plane.
Round your answer to the nearest hundredth.

Answer 1

To calculate the distance between the points A = (3, 0) and F = (-2, -3), we can use the distance formula:

distance = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) = (3, 0) and (x2, y2) = (-2, -3).

Substituting these values, we get:

distance = √[(-2 - 3)² + (-3 - 0)²]

distance = √[(-5)² + (-3)²]

distance = √[25 + 9]

distance = √34

Rounding to the nearest hundredth, we get:

distance ≈ 5.83

Therefore, the distance between the points A = (3, 0) and F = (-2, -3) in the coordinate plane, rounded to the nearest hundredth, is approximately 5.83 units.