… if we join the origin to the points (r,s) and (u,v) .. then we have two triangles both of them wuld be right angle triangles … and the hypotenuse of the triangles wuld be the distance from the center … and the sides for the 2 triangle wuld be r, s for the first one and u,v for the second one ..f2001290 wrote:18. In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin ?
(1) r + s = 1
(2) u = 1 – r and v = 1 – s
Please Explain
so what the q basically asks is if r^2+s^2 = u^2+v^2 …
.. the first statement says that r+s=1 .. which does not really help .. so insufficient ..
… from the second statement we have
u^2= 1+r^2-2r
v^2=1+s^2-2s …
adding both of them we have u^2+v^2=2+r^2+s^2-2(r+s) .. so we have
(u^2+v^2) - (r^2+s^2) = 2 – 2(r+s) now remember if the 2 points were equidistant then (u^2+v^2) – (r^2+s^2) wuld be equal to 0 .. but for it to be 0 (r+s) has to be equal to 1 but we don’t have anything in the second statement that says so .. so second statement is also insufficient
now combine both the statement and from the first statement we have r+s=1 … and by substituting this in the eqn (u^2+v^2)-(r^2+s^2)=2-2(r+s) .. we get (u^2+v^2)-(r^2+s^2)=0 .. and that means the two points are equidistant from the origin .. so the answer is C .. post if any doubts ..
