In a rectangular coordinate system ,are the points (r,s) and (u,v)
equidistant from origin?
2)u=1-r and v=1-s
Kindly HELP solving this since im not able to get to the answer !!!
Origin is (0,0). Distance between origin and (r,s) is SQRT(r² + s²) and Distance between origin and (u,v) is SQRT(u² + v²)
so we have to prove if SQRT(u² + v²) = SQRT(r² + s²)
Now (1) is insufficient since it provides us NO information reg u and v
(2) u = 1-r and v=1-s
distance from (0,0) and (u,v) is = SQRT(u² + v²)
= SQRT((1-r)² + (1-s)²)
= SQRT(1 + r²- 2r + 1 + s² - 2s)
= SQRT(2 -2(r+s) + r² + s²)
Now we are stuck here. 2 also insufficient.
Combining 1 and 2 we get -- SQRT(u² + v²) = SQRT(2 -2(r+s) + r² + s²)
from 1 we get r+s =1 on substituting this in the above equation we get SQRT(u² + v²) = SQRT(r² + s²)
Hence the answer must be C
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