P(2,1) and Q(1,2) are points in a plane. Find the bearing of Q from P
no, since tan(225°) = 1
The bearing is (270+45)° = 315°
or, from the -y axis, (180+135)° = 315°
To find the bearing of point Q from point P, we can use the inverse tangent function. The bearing is the angle formed between the positive x-axis and the line segment connecting the two points P and Q.
First, let's find the slope of the line segment connecting points P(2,1) and Q(1,2).
Slope (m) = (y2 - y1) / (x2 - x1)
= (2 - 1) / (1 - 2)
= 1 / -1
= -1
Next, we need to find the angle formed between the positive x-axis and the line segment. We can use the inverse tangent (arctan) function to do this.
Bearing = arctan(m)
Bearing = arctan(-1)
Using a scientific calculator, we get:
Bearing ≈ -45°
Therefore, the bearing of point Q from point P is approximately -45°.
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.
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).