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**ASh****Guest**

I need to make line B parallel to line A. I have start and end coordinates of line A and start coordinate of line B. Can I calculate the end coordinate of line B to make it parallel to line A. I also have end X coordinat. So all I actually need is end Y.

Any suggestions? Thank you.

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Say your lines look like this: Y

/

Q /

/ /

/ /

/ /

/ X

/

/

P

You know the co-ordinates of P, Q and X and the x co-ordinate of Y.

Let's say that P is (a,b); Q is (c,d); X is (e,f) and Y is (g,h). You want to find h.

You know that the two lines are parallel and that means that their gradients are the same.

The gradient of a line is the amount of units that it moves up for every unit that it moves right.

The gradient of line PQ is (d-b)/(c-a) and the gradient of line XY is (h-f)/(g-e)

As these are the same, they can be combined into an equation: (d-b)/(c-a)=(h-f)/(g-e)

As we want to find h, we want to make it the subject of this equation.

Multiply by (g-e): (d-b)(g-e)/(c-a)=h-f

Add f: **h=(d-b)(g-e)/(c-a)+f**

And there's your y co-ordinate!

Why did the vector cross the road?

It wanted to be normal.

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**ASh****Guest**

Thank you very much. It was very helpful and clear. And easy, what's the most important :-)

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