Two points in the xy plane have cartesian coordinates (4.6,-10) and
(-10,3.2) I found the distance to be 19.68 but i need to find the angle between the line connecting the two points and the x-axis (measured counterclockwise from the x-axis) within the limits of -180 and +180 degrees).....
To find the angle between the line connecting the two points and the x-axis, you can use the arctan function.
First, let's find the slope of the line connecting the two points. The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points, let's calculate the slope:
m = (3.2 - (-10)) / (-10 - 4.6)
= 13.2 / -14.6
= -0.904
Next, we can use the arctan function to find the angle in radians:
θ = arctan(m)
Taking the arctan of -0.904 using a calculator, we get:
θ ≈ -42.64 degrees
Note that the arctan function only gives us an angle between -90 and 90 degrees. To obtain the angle within the limits of -180 and +180 degrees, we can use the slope of the line in combination with the coordinates of the points.
1. If the difference of the x-coordinates (x2 - x1) is positive and the difference of the y-coordinates (y2 - y1) is negative, the angle will be in the 2nd quadrant. To find the angle in the 2nd quadrant, subtract the angle obtained from the arctan function from 180 degrees (θ = 180 - |arctan(m)|).
2. If the difference of the x-coordinates (x2 - x1) is negative and the difference of the y-coordinates (y2 - y1) is positive, the angle will be in the 4th quadrant. To find the angle in the 4th quadrant, add the angle obtained from the arctan function to 180 degrees (θ = 180 + |arctan(m)|).
Taking into account the coordinates of the two points, let's determine the correct quadrant and calculate the final angle:
Difference of x-coordinates: -10 - 4.6 = -14.6
Difference of y-coordinates: 3.2 - (-10) = 13.2
Since the difference of the x-coordinates is negative and the difference of the y-coordinates is positive, the angle is in the 4th quadrant.
θ = 180 + |arctan(m)|
= 180 + |-42.64|
= 180 + 42.64
= 222.64 degrees
Therefore, the angle between the line connecting the two points and the x-axis (measured counterclockwise from the x-axis) within the limits of -180 and +180 degrees is approximately 222.64 degrees.