O(0,0),P(-2,-2) and Q(1,-2) are the vertices of a triangle,R is a point on PQ such hat PR:RQ=2*underroot2:underoot5,then or is:

1)a median of the triangle.

2)an altitude of the triangle

3)bisector of the angle at O

4)None of these

ANS:3)

If OR was the median, PR = RQ.

And thats certainly not true.

Hence (a) is incorrect.

If OR was the altitude,

PQ ⊥ OR,

that is,

(slope PQ) × (slope OR) = -1

But the product equals 0.

Hence (b) is also incorrect.

If OR would have been an angle bisector at O,

Ratio of distances of any point on OR to point on the pther sides would be constant.

Now, to prove,

take any general point on OP, OR and OQ.

Find (distance of point on OR to that on OP)/(distance of point on OR to that on OQ)

It will be equal to PR/RQ.

This will prove that OR is angle bisector at O.

A Bit lengthy. Try it out!!