Can You Calculate Angles from Graph Coordinates and Slopes?

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Calculating angles from graph coordinates and slopes is possible using the formula for the angle between two points, which is given by tan^(-1)((y2 - y1) / (x2 - x1)). The slope of a line, defined as rise over run, directly relates to the tangent of the angle. If a line does not intercept the x or y axis, the same principles apply, as the slope still provides the necessary information. Understanding these relationships allows for the determination of angles between various points on a graph. This method effectively utilizes the coordinates and slopes to calculate angles accurately.
darkelf
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Hi,

Is there a way of calulating the angles from the slope or coordinates of a graph. Say you have a bunch of x and y coordinates and you want to find the angles between those points at various coordinates (say every x,y ratio) can it be done?
How would you go about it?
 
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yes,why not. :)

Angle between lines joining (x_1,y_1) \&\(x_2,y_2)=tan^{-1}\left( \frac{y_2-y_1}{x_2-x_1}\right)
 
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Angles between lines joining? If you have a single slope that doesn't intercept at the x or y axis?
 
Have another look at skand's answer. Slope means rise over run, right? So if you have the slope, then you have the tangent of the angle.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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