spriya wrote:

In a rectangular coordinate system ,are the points (r,s) and (u,v)

equidistant from origin?

1)r+s=1

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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