Two points are in a Cartesian plane. The first has coordinates (2.34 m, -4.37 m) and the second (-2.69 m, 3.04 m).

Question

Cartesian: (x, y)

Polar: (r, θ)

*coordinates are in 1st plane*

A) What is the value of r in polar coordinates for the first point?

Answer 1

In polar coordinates, r tells us us just the distance of the point from the origin, then theta tells us the direction.

1. I'd start by drawing point one on an x-y plane. It will be in the 4th quadrant.
2. Now sketch a right triangle to that point
3. The horizontal leg is the x component (2.34 m)
4. The vertical leg is the y component (-4.37 m)
5. The hypotenuse is your r value
6. Use Pythagorean theorem to find the r value
7. (2.34)² + (-4.37)² = r²
8. Check: r should be greater than each of the legs of the triangle.