Question

The cartesian coordinates of a point in the xy plane are x = −7.11 m, y = −4.41 m. Find the distance r from the point to the origin. Answer in units of m.

Answer 1

Explanation:

Use Pythagorean theorem:

r² = x² + y²

r² = (-7.11 m)² + (-4.41 m)²

r = 8.37 m

Use trig to find the angle.

tan θ = y / x

tan θ = (-4.41 m) / (-7.11 m)

θ = 31.8° or 211.8°

Since x is negative and y is negative, the point is in the third quadrant, so θ = 211.8°.

Or, if we subtract 360°, θ = -148.2°.