Quick math question

[Jay59express]

This is kind of embarassing, but I have what I think is a fairly simple math question to ask:

Given a line in a 2D plane that I know the (x,y) coordinates of two points (A and C), what is the equation to find a point (B) between them. I know the distance between A and C as well as between A and B and also B and C.

I know the equation for the midpoint, but would like to find the X,Y of any point between A and C.

Thanks!

 

[habib89]

distance = sqrt(a^2+c^2) or something like that

 

[StrangerGuy]

Ah nvm

 

[Suspicious-Teach8788]

Slow way:

I'm sure there's faster, and a lot of ppl aren't really reading your problem correctly.

Get a slope function in there. Solve for the coordinates... AC and BC are the same slope. Then calculate distance. The total distance = AC, etc...

 

[Kelemvor]

hmm

Gotta find the ratio of the angle that makes up the line and then just find any 2 points with the right ratio.

Basically take one point and pretend it's right at the X,Y junction (0,0) then find where the other point is in relation to that. Get the ratio, then find any point with that ratio but then add the first coordinate to it.... or something like that.

 

[akenbennu]

Use the slope intercept form of the equation.

y= mx + b where m is the slope of the line and b is the y-intercept

Let A be described by point (x1, y1)
Let C be described by point (x2, y2)

m = (y2-y1)/(x2-x1)

You now have y = ((y2-y1)/(x2-x1))*x + b

Substitute one of your known points into the equation and solve it for b, then you have the equation describing any point on the line containing points A and C.

 

[Jay59express]

Thanks akenbennu, but I don't have either an X or a Y for point B, only its distance from point A and point C

 

[dullard]

Let (xa, ya) be the location of point A.
Let (xc, yc) be the location of point C.

The midpoint, B, is halfway from A to C. Thus B is at: ([xa+xc]/2, [ya+yc]/2).

It is as simple as that. Extend that logic for any other fraction of a distance from A to C. Do you need me to do it for you?

Edit: I'll do it anyways.

Start at point A. Suppose you want to go a distance dAB from A. Suppose that the total distance is dAC. Thus, you are going a fraction, dAB/dAC, from A to C. So your point B starts at (xa, ya) and moves a distance dAB/dAC in the direction of C. Point B is at:

(xa, ya) + (dAB/dAC*[xc-xa], dAB/dAC*[yc-ya])

Adding them together, point B is at:

(xa+dAB/dAC*[xc-xa], ya+dAB/dAC*[yc-ya])

 

[Jay59express]

Thanks a lot dullard (and everyone else)

 

[dullard]

Originally posted by: Jay59express
Thanks a lot dullard (and everyone else)

You are always welcome.

 

[akenbennu]

You can use the ratios to find the distances.

Distance of line AB/distance of line AC = (x1-xb)/(x1-x2)

Solve for xb. Plug xb back into the equation in the form y=mx+b for the line to get yb. You now have the coordinated for point B (xb,yb)