Question

(See diagram) The gradient of the line joining the origin to the point A is 1/2. The distance between A and the origin is sqrt 2205. What are the coordinates of A?

Answer 1

Let the coordinate of point A be (x,y) .

ANd the given slope is 1/2 .

That is

`(y-0)/(x-0) = (1)/(2) \\ (y)/(x) = (1)/(2) \\ x=2y`

And the distance between O and A is sqrt 2205, that is

`√(x^2 +y^2) = \sqrt {2205} \\ x^2 + y^2 = 2205`

Substituting 2y for x, we will get

`(2y)^2+y^2 =2205 \\ 5y^2 = 2205 \\ y^2 = 441 \\ y=21`

And we have

`x=2y \\ x=2(21) \\ x=42`

So the point is (42,21)