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In the xy-plane, which of the following points is the greatest distanc

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In the xy-plane, which of the following points is the greatest distanc [#permalink]

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New post 13 Dec 2017, 07:39
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

96% (00:28) correct 4% (01:39) wrong based on 27 sessions

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Kudos [?]: 139606 [0], given: 12794

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In the xy-plane, which of the following points is the greatest distanc [#permalink]

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New post 13 Dec 2017, 08:23
Bunuel wrote:
In the xy-plane, which of the following points is the greatest distance from the origin?

(A) (0,3)
(B) (1,3)
(C) (2,1)
(D) (2,3)
(E) (3,0)

Points on the axes lie on the same line as the origin, and have the same x- or y-coordinates. Subtract 0 from the non-zero coordinate.

For other points, you could construct a right triangle with horizontal and vertical legs that = length of coordinates.

(A) (0,3)
From y-coordinates of (0,3) and (0, 0)
Distance \(= (3 - 0) = 3\)

(B) (1,3)
Distance, d, from a right triangle with leg = 1 and leg = 3 (Pythagorean theorem):
\((1^2 + 3^2) = d^2\)
\((1 + 9) = 10 = d^2\)
Distance \(=
\sqrt{10}\)

(C) (2,1)
Distance, d, from a right triangle:
\((2^2 + 1^2) = (4 + 1) = 5 = d^2\)
Distance \(=
\sqrt{5}\)

(D) (2,3)
Distance, d, from a right triangle:
\((2^2 + 3^2) = (4 + 9) = 13 = d^2\)
Distance \(=
\sqrt{13}\)

(E) (3,0)
From x-coordinates of (3,0) and (0,0)
Distance \(= (3 - 0) = 3\)

Answer D
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Re: In the xy-plane, which of the following points is the greatest distanc [#permalink]

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New post 13 Dec 2017, 21:37
D it is
Use the Pythagorean theorem and put values of x and y
x^2 + y^2 = c^2
the option that has highest value of C is the answer
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Kudos [?]: 66 [0], given: 275

Re: In the xy-plane, which of the following points is the greatest distanc   [#permalink] 13 Dec 2017, 21:37
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