Find the angle between the line y=2x and the points (-1;7/3 ) and (0;2)
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See previous post: Tue,8-6-13,12:09 PM
To find the angle between a line and two given points, you can follow these steps:
Step 1: Determine the slope of the line through the equation y = 2x.
The given line has a slope of 2 because its equation is in the form y = mx, where m represents the slope.
Step 2: Calculate the slope of the line passing through the two given points.
The slope between two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).
Using the points (-1, 7/3) and (0, 2), we can calculate the slope:
m = (2 - 7/3) / (0 - (-1))
= (2 - 7/3) / (0 + 1)
= (2 - 7/3) / 1
= (6/3 - 7/3) / 1
= (-1/3) / 1
= -1/3
Step 3: Determine the angle between the two lines.
The angle between two lines with slopes m1 and m2 is given by the formula: θ = arctan((m2 - m1) / (1 + m1 * m2)).
Using the slope of the line y = 2x (m1 = 2) and the calculated slope (m2 = -1/3), we can now find the angle:
θ = arctan((-1/3 - 2) / (1 + 2 * (-1/3)))
= arctan((-7/3) / (1 - 2/3))
= arctan((-7/3) / (3/3 - 2/3))
= arctan((-7/3) / (1/3))
= arctan(-7)
The result is the angle measured in radians. To convert it to degrees, you can use the conversion factor: 180° / π radians.
Therefore, the angle between the line y = 2x and the points (-1, 7/3) and (0, 2) is approximately -80.537°.