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In the coordinate plane, points (a, b) and (c, d) are equidi
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30 Sep 2018, 15:58
30 Sep 2018, 15:58
Expert Reply
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Question Stats:
67% (01:02) correct
32% (01:34) wrong based on 145 sessions
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In the coordinate plane, points (a, b) and (c, d) are equidistant from the origin.
\(|a| > |c|\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(|a| > |c|\)
Quantity A |
Quantity B |
|b| |
|d| |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: In the coordinate plane, points (a, b) and (c, d) are equidi
[#permalink]
10 Dec 2018, 17:41
10 Dec 2018, 17:41
5
Answer: B
What we have:
Distance from (a,b) to origin (0,0) = √((a-0)^2 + (b-0)^2) = √(a^2 + b^2)
Distance from (c,d) to origin (0,0) = √((c-0)^2 + (d-0)^2) = √(c^2 + d^2)
It is said that points (a, b) and (c, d) are equidistant from the origin. It means their distances from origin are equal, so:
√(a^2 + b^2) = √(c^2 + d^2) , both sides to power2:
a^2 + b^2 = c^2 + d^2
As it is said that |a| > |c| so we can conclude that |a|^2 > |c|^2 [They are both positive, thus when they are in the same power, their comparison result will be just the same as when the power is 1.]
Now that we know a^2 > c^2 and a^2 + b^2 = c^2 + d^2, so we can construe that b^2 is less than d^2 and so |b| is less than |d| (b and d don’t necessarily have the same relation) B is bigger than A
What we have:
Distance from (a,b) to origin (0,0) = √((a-0)^2 + (b-0)^2) = √(a^2 + b^2)
Distance from (c,d) to origin (0,0) = √((c-0)^2 + (d-0)^2) = √(c^2 + d^2)
It is said that points (a, b) and (c, d) are equidistant from the origin. It means their distances from origin are equal, so:
√(a^2 + b^2) = √(c^2 + d^2) , both sides to power2:
a^2 + b^2 = c^2 + d^2
As it is said that |a| > |c| so we can conclude that |a|^2 > |c|^2 [They are both positive, thus when they are in the same power, their comparison result will be just the same as when the power is 1.]
Now that we know a^2 > c^2 and a^2 + b^2 = c^2 + d^2, so we can construe that b^2 is less than d^2 and so |b| is less than |d| (b and d don’t necessarily have the same relation) B is bigger than A
General Discussion
Re: In the coordinate plane, points (a, b) and (c, d) are equidi
[#permalink]
28 Oct 2018, 11:48
28 Oct 2018, 11:48
The answer is B
