gmattesttaker2 wrote:Hello,
Can you please assist with this:
In a coordinate system, how many points (x,y) simultaneously satisfy the conditions
|x| + |y| ≤ 1 and x^2 + y^2 = 1?
(A) exactly one
(B) exactly two
(C) exactly three
(D) exactly four
(E) infinite points
OA: D
Thanks,
Sri
x² + y² = r² is the equation of circle centered at the origin.
Thus:
x² + y² = 1 is a circle centered at the origin with a radius of 1:
The 4 points shown -- (0,1), (1,0), (0,-1), and (-1,0) -- all satisfy the constraint that |x| + |y| ≤ 1.
If we choose ANY OTHER POINT on the circle, we get something like this:
Since the hypotenuse of the yielded triangle has a length of 1, the sum of the two legs -- |x| + |y| -- must be GREATER than 1.
Thus, only 4 points on circle x² + y² = 1 satisfy the constraint that |x| + |y| ≤ 1:
(0,1), (1,0), (0,-1), and (-1,0).
The correct answer is
D.
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