P(2,1) and Q(1,2) are points in a plane. Find the bearing of P from Q
To find the bearing of P from Q, we need to find the angle between the line passing through P and Q, and the north direction.
First, let's find the slope of the line passing through P and Q:
slope = (y2 - y1) / (x2 - x1)
slope = (2 - 1) / (1 - 2)
slope = -1
Next, we can find the angle between the line and the north direction by taking the arctan of the slope:
angle = arctan(-1)
Using a calculator, we find that angle ≈ -45°.
However, bearings are usually given in degrees clockwise from the north direction. To convert our angle to bearing, we can add 360° and then take the remainder when divided by 360°:
bearing = (angle + 360) % 360
bearing ≈ 315°
Therefore, the bearing of P from Q is approximately 315°.
To find the bearing of point P from point Q, we can use the following steps:
Step 1: Calculate the change in x-coordinate (Δx) and the change in y-coordinate (Δy) between the two points.
Δx = x2 - x1
Δy = y2 - y1
In this case:
Δx = 1 - 2 = -1
Δy = 2 - 1 = 1
Step 2: Use the arctan function to calculate the angle θ:
θ = arctan(Δy/Δx)
Substituting the values:
θ = arctan(1/-1)
Step 3: Convert the angle from radians to degrees.
Convert θ from radians to degrees using the equation: degrees = radians × (180/π)
Substituting the value of θ:
degrees = arctan(1/-1) × (180/π)
Finally, calculate the bearing from Q to P by adding 180 degrees to the result.
Therefore, the bearing of P from Q is approximately 225 degrees.