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 deltaxrayI 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:
andSo the equation of the locus of Q is:
Grandad