Final answer:
To find the distance between two points A and B in the Cartesian plane, we can use the formula Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2). For the given points A(2.00 m, -4.00 m) and B(-3.00 m, 3.00 m), the distance between them is approximately 8.60 m. The polar coordinates of point A(2.00 m, -4.00 m) are approximately (4.47 m, -63.43°).
Step-by-step explanation:
To find the distance between two points A and B in the Cartesian plane, we can use the formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For the given points A(2.00 m, -4.00 m) and B(-3.00 m, 3.00 m), we have:
x1 = 2.00 m, y1 = -4.00 m
x2 = -3.00 m, y2 = 3.00 m
Substituting these values into the formula:
Distance = sqrt((-3.00 - 2.00)^2 + (3.00 - (-4.00))^2)
= sqrt((-5.00)^2 + (7.00)^2)
= sqrt(25.00 + 49.00)
= sqrt(74.00)
= 8.60 m
Hence, the distance between points A(2.00 m, -4.00 m) and B(-3.00 m, 3.00 m) is 8.60 m.
The polar coordinates of a point (r, θ) can be found using the formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y / x)
For point A(2.00 m, -4.00 m):
r = sqrt(2.00^2 + (-4.00)^2)
= sqrt(4.00 + 16.00)
= sqrt(20.00)
≈ 4.47 m
θ = arctan((-4.00) / 2.00)
= arctan(-2.00)
≈ -63.43°
Hence, the polar coordinates of point A(2.00 m, -4.00 m) are approximately (4.47 m, -63.43°).