How do you determine if a point lies to the left or right of a line?

Answer 1

The answer below the horizontal line is pretty involved and you may not need all of that, but it is left in the answer. Here is a simple way:

Take a line in the form y = mx + b, and rearrange it to be x = y/m - b/m.

For example, if you had y = 5x - 2, the rearranged version is x = y/5 + 2/5 {note that it is minus in the first one (b=-2) and plus in the second}

Now say that you have a point (2,3) and you want to see which side of the line it is. Plug in the y value {3}:

• x = 3/5 + 2/5 = 5/5 = 1.
• Your point has an x-value of 2, which is greater than 1, so the point is to the right of the line {the point (1,3) lies on the line}.

I hope you will be satisfied by the following explanation:

suppose the equation of your line is ax+by=c;

then points with ax +by>c lie on opposite side of your line when compared to points which have ax + by

now arises the issue of left or right ....by now you must have figured out that by using the above method and (0,0) you can easily calculate that....thaink over it dear....or else mail me at

anubhavgupta.iitd@gmail.com

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a complete solution.

because of the terms "left" and "right" we need a direction for the line

let 2 points on the line

A(x1,y1) and B(x2,y2). we are moving from A to B

and

M(x0,y0) is a point

and

a little geometry

m=(x2-x1)*(y2-y1) a rectangular

p1=(x0-x1)*(y0-y1) a second rectangular

p2=(x2-x0)*(y2-y0) and another

p3=(x2-x0)*(y0-y1)*2 now two rectangulars

if m=p1+p2+p3 the point is on the line

if m

if m>p1+p2+p3 the point is right

if there is something you dont understand emailme tsirospan@gmail.com

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This can be simplified to calculating (x0 - x1) * (y2 - y1) - (x2 - x1) * (y0 - y1) which is the same as m - p1 - p2 - p3.

Whether the first or the second answer is better for you depends on whether you have the equation of the line or just two points on it.

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one more time.

A(x1,y1) B(x2,y2) a line segment with length L=sqrt( (y2-y1)^2 + (x2-x1)^2 )

and a point M(x,y)

making a transformation of coordinates in order to be the line AB the new X axis and the point A to be the new origin (ie (0,0)) ,

we have the new coordinates of the point M(x,y)

which are

newX = ((x-x1)*(x2-x1)+(y-y1)*(y2-y1))/L from (x-x1)*cos(t)+(y-y1)*sin(t) where cos(t)=(x2-x1)/L, sin(t)=(y2-y1)/L

newY = ((y-y1)*(x2-x1)-(x-x1)*(y2-y1))/L from (y-y1)*cos(t)-(x-x1)*sin(t)

Because "left" is the side of axis X with positive Y, if the newY (which is the distance of M from AB) is positive, then it is on the left side of AB

You may omit the division by L (a positive number), if you only want the sign.

If the newX is positive the M is on the right of the new Y axis, at a distance newX