Question

Ing the pair of points (1,-6) and (-1,-6)

Answer 1

The distance between points A and B is sqrt(74), and the polar coordinates of point A are sqrt(20) and atan2(-4.00, 2.00).

Step-by-step explanation:

The distance between two points in the Cartesian plane can be found using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For the points A(2.00, -4.00) and B(-3.00, 3.00), the distance is:

d = sqrt(((-3.00) - 2.00)^2 + (3.00 - (-4.00))^2)

d = sqrt((-5)^2 + (7)^2) = sqrt(25 + 49) = sqrt(74).

The polar coordinates of point A can be found using:

r = sqrt(x^2 + y^2)

θ = atan2(y, x)

For point A(2.00, -4.00), r = sqrt((2.00)^2 + (-4.00)^2) = sqrt(4 + 16) = sqrt(20) and θ = atan2((-4.00), (2.00)).