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

$\frac{y-0}{x-0} = \frac{1}{2} \\ \frac{y}{x} = \frac{1}{2} \\ x=2y$

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

$\sqrt{x^2 +y^2} = \sqrt {2205} \\ x^2 + y^2 = 2205$

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)