Question

The coordinate of point P on line l is 2 and that of Q is -4 . If R[r] is a third point on I such that P−Q−R and QR=2, find:

a) PR [4]
b) the coordinate r of point R. [4]

Answer 1

To find polar coordinates from Cartesian coordinates, calculate the distance from the origin and the angle with the positive x-axis. The distance between points in the Cartesian plane is determined using the distance formula.

Step-by-step explanation:

The question is asking us to find the polar coordinates of a point given its Cartesian coordinates and to determine the distance between points in the Cartesian plane. To convert from Cartesian coordinates to polar coordinates, we use the equations r = √(x² + y²) for the distance from the origin, and θ = tan⁻¹(y/x) for the angle relative to the positive x-axis. The distance between two points in the Cartesian plane is given by the equation d = √((x2 - x1)² + (y2 - y1)²).

For example, to find the polar coordinates of point A(2.00 m, -4.00 m), we calculate the distance r as r = √(2.00² + (-4.00)²) and the angle θ by θ = tan⁻¹(-4.00/2.00). To find the polar coordinates for point B(-3.00 m, 3.00 m), the process would be similar. The distance between points A and B can be found by substituting the respective x and y values into the distance formula above.