# Math Help - Simple problem... help please.

1. ## Simple problem... help please.

Hi,

I'm sure this is really simple but my brain doesn't seem to want to work and it is around 20 years since I tried something like this.

I have a line, Line A. I know the x and y coordinates of its start and end points and its length. I also know its angle with the positive x-axis.

I need to create line B. Line B must be perpendicular to line A and must start at either the start or end point of line A. I will know the length of line B.

So, given that I know the length, start point, and gradient of line B (negative reciprocal of line A’s gradient), is there some magic formula that I can feed these numbers in to in order to find the x,y coordinates of the end point of line B?

I was hoping there was some simple formula that I could just feed the values I know of line B into and get its end coordinates.

Any help would be greatly appreciated.

Chicka.

2. Try the distance formula. [LaTeX ERROR: Convert failed]

3. Originally Posted by Chicka
Hi,

I'm sure this is really simple but my brain doesn't seem to want to work and it is around 20 years since I tried something like this.

I have a line, Line A. I know the x and y coordinates of its start and end points and its length. I also know its angle with the positive x-axis.

I need to create line B. Line B must be perpendicular to line A and must start at either the start or end point of line A. I will know the length of line B.

So, given that I know the length, start point, and gradient of line B (negative reciprocal of line A’s gradient), is there some magic formula that I can feed these numbers in to in order to find the x,y coordinates of the end point of line B?

I was hoping there was some simple formula that I could just feed the values I know of line B into and get its end coordinates.

Any help would be greatly appreciated.

Chicka.
Hello,

I'll put some flesh to the more or less bony hint which janvdl gave to you:

Let the equation of line B be: y = mx + b
and let the endpoint of B be: $E(x_E, y_E)$ that means $E(x_E, mx_E + b)$

Now use the distance formula (without the square root) and the point A from line A:

$d^2 = (length)^2=(x_A-x_E)^2+(y_A - (mx_E + b))^2$

That is an equation with only $x_E$ unknown.

4. Thanks for the help so far, I'll see what I can do with it.