P(2,1) and Q(1,2) are points in a plane. Find the bearing of Q from P

Answer 1

We can use trigonometry to find the bearing of Q from P.

First, we need to find the angle that the line segment PQ makes with the x-axis. We can use the tangent function to do this:

tan(θ) = opposite/adjacent

where θ is the angle, opposite is the change in y-value (from P to Q) and adjacent is the change in x-value (from P to Q).

In this case, opposite = 2 - 1 = 1 and adjacent = 1 - 2 = -1. So:

tan(θ) = 1/-1 = -1

We need to find the angle whose tangent is -1. This is the angle between the line segment PQ and the negative y-axis (since the tangent is negative).

This angle is 135 degrees (or π/4 radians) in the third quadrant.

To find the bearing, we need to measure the angle clockwise from the north direction. So we subtract the angle we found from 360 degrees:

360 - 135 = 225 degrees

Therefore, the bearing of Q from P is 225 degrees.

Answer 2

no, since tan(225°) = 1
The bearing is (270+45)° = 315°
or, from the -y axis, (180+135)° = 315°

Answer 3

You are correct. Thank you for catching the error in my previous answer.

tan(θ) = 1/-1 = -1

The angle with a tangent of -1 is actually 135 degrees (as you noted) in the third quadrant. To find the bearing, we need to measure the angle clockwise from the north direction.

360 - (135 + 90) = 135

Therefore, the bearing of Q from P is 135 degrees or (360 - 135) = 225 degrees to be consistent with the standard practice of expressing the bearing clockwise from the north direction. The bearing can also be expressed as (180 + 135) degrees, as you mentioned, since 135 degrees is the angle between the negative y-axis and line segment PQ in the third quadrant.

The correct answer is that the bearing of Q from P is 135 degrees or 225 degrees (clockwise from the north direction).