Algorithm problem involving 3 points and 3 lines in the x,y plane

[sHatDowN]

Homework Statement

ArcTan Algorithm

Relevant Equations

Need to know how to implement arctan in algorithm

1- Coordinates of two points are given in x and y plane.
A(x1,y1), B(x2,y2)
Calculate the angle between the two lines passing through each of these points with the origin of linear coordinates.
2- If a line passes between the two points A and B above, does point C lie on this line?
C(x3,y3)

how to implement this algorithm?

 

[BvU]

Homework Statement:Algorithm
Relevant Equations: Algorithm

how to implement this algorithm?

Make a sketch

And find the exact problem statement. Not just the word algorithm

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[sHatDowN]

It's my idea :
arctan(y1/y2)
It's math idea but i don't know how to implement with algorithm

 

[Mark44]

1- Coordinates of two points are given in x and y plane.
A(x1,y1), B(x2,y2)
Calculate the angle between the two lines passing through each of these points with the origin of linear coordinates.

I think I understand what you're asking, but it's unclear. A better description would be: Calculate the angle between two lines that pass through the origin and points A and B.

2- If a line passes between the two points A and B above, does point C lie on this line?
C(x3,y3)

Also unclear. Are the coordinates of point C given? There are an infinite number of lines that pass between points A and B. Without more information, I don't think this is solvable.

how to implement this algorithm?

You're not implementing an algorithm -- you're attempting to solve a very vaguely defined problem.

arctan(y1/y2)
It's math idea but i don't know how to implement with algorithm

It's not clear to me what, if anything, the arctangent has to do with the problem you're trying to solve.

 

[FactChecker]

It's my idea :
arctan(y1/y2)
It's math idea but i don't know how to implement with algorithm

You should become familiar with the problem of arctan(y/x) when it is not true that both y and x are positive. The problem is that arctan(y/x) = arctan(-y/-x) and arctan(y/-x) = arctan(-y/x), so arctan(y/x) is not a very simple indicator of the angle of a radial line from the origin. You would need to do a lot of additional checking about the signs of x and y.
In computer program languages this problem is greatly simplified by the function atan2( y, x). It accounts for the signs of the inputs correctly.
All angles are in radians, ##r##, where ##-\pi \lt r \le \pi##.
atan2( y1, x1) would give you the counterclockwise angle from the positive X-axis to the line (0, A). (Negative radians is going clockwise)
Similarly, atan2( y2, x2) would give you the counterclockwise angle from the positive X-axis to the line (0, B).
Can you use that to solve the problem?

 

[valenumr]

Homework Statement:: ArcTan Algorithm
Relevant Equations:: Need to know how to implement arctan in algorithm

1- Coordinates of two points are given in x and y plane.
A(x1,y1), B(x2,y2)
Calculate the angle between the two lines passing through each of these points with the origin of linear coordinates.
2- If a line passes between the two points A and B above, does point C lie on this line?
C(x3,y3)

how to implement this algorithm?

Are you asking to show whether or not (x3,y3) lies on a line between (x1,y1) and (x2,y2)?

This is algebra.

 

[valenumr]

Homework Statement:: ArcTan Algorithm
Relevant Equations:: Need to know how to implement arctan in algorithm

1- Coordinates of two points are given in x and y plane.
A(x1,y1), B(x2,y2)
Calculate the angle between the two lines passing through each of these points with the origin of linear coordinates.
2- If a line passes between the two points A and B above, does point C lie on this line?
C(x3,y3)

how to implement this algorithm?

By definition in 2 dimensional euclidean geometry, a line that passes between two points will intersect with the line defined by them. You've only given one point for the intersecting line, so ...

 

[FactChecker]

For part 2, if the angle of the line from A to B differs from the angle of the line from A to C by a multiple of ##\pi##, then C is on the line through A and B.