# Thread: Find Coordinates of point given length and formula of line

1. ## Find Coordinates of point given length and formula of line

Okay, this is a coordinate geometry question I think. It is question 11 from IGCSE Additional Mathematics - October/November 2007 Paper 2.

This is part two of the question. In part one, I found the length of a line OB. It starts from the origin and goes until it meets point B. I have to find the coordinates of B. The formula of the line is y=2x and the length is 2√5. As I said before, it goes through the origin.

It is part of a right angled triangle BOA, with BA being the hypotenuse, OA being the second longest side and OB the shortest side. Length of OA is 3√5 and coordinate A is (6,-3). BO and AO meet to form the 90deg angle which makes it a right angled triangle.

Please help me figure this out. I have tried but cannot find a solution. I need to know in less than an hour

2. The distance from the origin is $2\sqrt5$

The line concenrned is y = 2x.

At any point (x, y) on the line, the distance is $d^2 = x^2 + y^2$

Using what you've got, you have:

$(2\sqrt5)^2 = x^2 + y^2$

$20 = x^2 + y^2$

Now, you have got the line y = 2x.

Use simultaneous equations to find the x coordinate of B.

Depending on where point B lies, relative of the origin, you can have 2 different answers.

3. Thanks alot. I was able to do it.

4. You're welcome