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
Tricky question!
Target question: Are the points (r,s) and (u,v) equidistant from the origin?
Statement 1: r + s = 1
There's no info about the point (u,v)
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: u = 1 - r and v = 1 - s
There are several sets of coordinates that meet this condition. Here are two:
Case a: (r,s) = (1,0), which means (u,v) = (0,1). In this case
the points (r,s) and (u,v) are equidistant from the origin
Case b: (r,s) = (1,1), which means (u,v) = (0,0). In this case
the points (r,s) and (u,v) are not equidistant from the origin
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 2 tells us that u = 1 - r and v = 1 - s
We can rearrange these two equations to get
u + r = 1 and
v + s = 1
Let's compare each of these equations with the equation in statement 1 (r + s = 1)
u + r = 1
s + r = 1
Subtract equations to get: u - s = 0, which means
u = s
v + s = 1
r + s = 1
Subtract equations to get: v - r = 0, which means
v = r
If
r = v and
s = u, then
the points (r,s) and (u,v) are equidistant from the origin
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
