DS coordindate geometry

[Gopaleie2k4]

Can some one explain the answer for this

Thanks & Regards
Gopalakrishnan M

[prasadjoglekar]

(1) is clearly not sufficient.

(2) is also not sufficient - substitute (r, s) as (0,0), then (u,v) is (1,1) - i.e. distances are not the same. But substitute (r,s) as (1,0), then (u,v) is (0, 1) - i.e. the distances are the same.

Now, together, I think they are sufficient to solve. What follows is mostly algebra.

The distance for (r,s) from origin is sqrt(r^2 + s^2)

The distance for (u,v) from origin in terms of r,s is:
sqrt[(1-r)^2 + (1-s)^2].
Simplify => sqrt(r^2 + s^2 - 2r - 2s +2).
Substitue r+s = 1 => sqrt(r^2 + s^2).

Which is the same as the distance for (r,s).

Hence (C)

[rros0770]

Hey prasadjoglekar,

Good insight into this question. I'm not familiar with that formula used to determine the distance of a point from the origin, the sqrt(r^2 + s^2) formula. Is this a general rule/formula to determine where a point lies in relation to the origin? Thanks