## Point of two intersecting lines at 90 degree Topic is solved

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mast4rwang
Posts: 141
Joined: 19 Jul 2017, 09:59

### Point of two intersecting lines at 90 degree

Hello guys, I am trying to write a script which asks to input A(x;y) and B(x1;y1) and it displays the end result, which is coordinates of c(a;b). I can get lengths of lines so easily because they make right triangles, but when it comes to coordinates I am lost on what to do
Could someone help me out?

This is an illustration:
Spoiler
teadrinker
Posts: 1067
Joined: 29 Mar 2015, 09:41
Contact:

### Re: Point of two intersecting lines at 90 degree  Topic is solved

Hi, mast4rwang. It's just school mathematics.

We have the line passing through two points (x1, y1) and (x2, y2), and point B(x3, y3)

The general equation of line with two points is
(y1 - y2)*X + (x2 - x1)*Y + (x1*y2 - x2*y1) = 0
In our case x2 and y2 are equal 0, therefore
y1*X - x1*Y = 0

If x1 equal 0, then the intersection point x = 0, y = y3.
If y1 equal 0, then x = x3, y = 0.

Else
Y = (y1/x1)*X
y1/x1 is the line's slop, hence the perpendicular's slop is -x1/y1
Then the perpendicular's equation is
Y - y3 = -x1/y1(X - x3)

Now to get the intersection point we need to solve the set of equations:
Y - y3 = -x1/y1(X - x3)
Y = (y1/x1)*X

(y1/x1)*X - y3 = -x1/y1(X - x3)
-(y1**2/x1**2)*X + y1/x1*y3 = X - x3
X + (y1**2/x1**2)*X = y1/x1*y3 + x3

X = (y1/x1*y3 + x3)/(y1**2/x1**2 + 1)
Y = (y1/x1)*X

Code: Select all

``````coords := GetIntersection( {x: -2, y: 2}, {x: 1, y: 3} )

MsgBox, % "X = " . coords.x . A_Tab . "Y = " . coords.y

GetIntersection(point1, point2)  {
if (point1.x = 0)
Return {x: 0, y: point2.y}

if (point1.y = 0)
Return {x: point2.x, y: 0}

X := (point1.y/point1.x * point2.y + point2.x)/( (point1.y**2)/(point1.x**2) + 1 )
Y := point1.y/point1.x * X

Return {x: X, y: Y}
}``````
mast4rwang
Posts: 141
Joined: 19 Jul 2017, 09:59

### Re: Point of two intersecting lines at 90 degree

Cheers, teadrinker!
BoBo
Posts: 2519
Joined: 13 May 2014, 17:15

### Re: Point of two intersecting lines at 90 degree

No doubt about that: "It's tea time!"
teadrinker
Posts: 1067
Joined: 29 Mar 2015, 09:41
Contact:

### Re: Point of two intersecting lines at 90 degree

mast4rwang
Posts: 141
Joined: 19 Jul 2017, 09:59

### Re: Point of two intersecting lines at 90 degree

Well, one thing is certain: Teadrinker, you got a new fan

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