Thread: Locus

P(x,y) is a variable point on the line 2x-3y+6 = o, and the point Q divides OP in the ratio 3:2. Show that Q has co ordinates ( \frac{3}{5}, \frac{2/5) (x+3)) hence find the locus of Q.

Thanks

Hello deltaxray

Originally Posted by deltaxray

P(x,y) is a variable point on the line 2x-3y+6 = o, and the point Q divides OP in the ratio 3:2. Show that Q has co ordinates ( \frac{3}{5}, \frac{2/5) (x+3)) hence find the locus of Q.

Thanks

I think you mean that Q has coordinates:

By similar triangles (or using the formula that you'll find in this post), the point Q that divides OP, where P is , in the ratio is

But if lies on the line , then

So Q is:

i.e.

So, if the coordinates of Q are , then:

and

So the equation of the locus of Q is:

Grandad