Answer: Therefore, the bearing of point A is approximately 73.74° with respect to the positive x-axis
Explanation: To determine the distance between points A(2,-5) and B(6,8), we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using this formula, we can calculate the distance between A and B as follows:
d = √((6 - 2)^2 + (8 - (-5))^2)
= √((4)^2 + (13)^2)
= √(16 + 169)
= √185
≈ 13.60
Therefore, the distance between points A and B is approximately 13.60 units.
Now, let's move on to the second part of the question. The bearing of A refers to the direction or angle between the line segment AB and the positive x-axis. To find the bearing of A, we can use trigonometry.
We'll start by finding the angle that the line segment AB makes with the positive x-axis. We can use the arctangent function to find this angle. The arctangent function gives us the angle whose tangent is equal to the slope of the line segment AB.
First, we calculate the slope of the line segment AB using the formula:
m = (y2 - y1)/(x2 - x1)
m = (8 - (-5))/(6 - 2)
= 13/4
Next, we find the arctangent of the slope to get the angle:
angle = arctan(13/4)
≈ 73.74°
Therefore, the bearing of point A is approximately 73.74° with respect to the positive x-axis