tonebeeze wrote:Can someone walk me through this problem. Thanks
140. 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
We can plug in values.
Statement 1: r+s = 1.
No information about (u,v).
Insufficient.
Statement 2: u = 1-r and v = 1-s.
Let r=1, u = 1-1 = 0.
Let s=1, v = 1-1 = 0.
Then (r,s) = (1,1) and (u,v) = (0,0).
Are (1,1) and (0,0) equidistant from the origin? No.
Let r=1, u = 1-1 = 0.
Let s=0, v = 1-0 = 1.
Then (r,s) = (1,0) and (u,v) = (0,1).
Are (1,0) and (0,1) equidistant from the origin? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.
Statements 1 and 2 combined:
Statement 1: r+s = 1.
Statement 2: r+u = 1.
Thus, r+s = r+u.
Thus, s=u.
Statement 1: r+s = 1.
Statement 2: v+s = 1.
Thus, r+s = v+s.
Thus, r=v.
Thus, (r,s) = (v,u), indicating that the two points will be equidistant from the origin.
Sufficient.
The correct answer is
C.
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