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# In the figure above, if the x-coordinate of point R is 5, and the leng

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
In the figure above, if the x-coordinate of point R is 5, and the leng  [#permalink]

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13 Dec 2017, 20:05
00:00

Difficulty:

5% (low)

Question Stats:

91% (00:56) correct 9% (00:00) wrong based on 35 sessions

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In the figure above, if the x-coordinate of point R is 5, and the length of OR is 7, then the y-coordinate of point R is

(A) 2√3
(B) 4
(C) 2√6
(D) 4√3
(E) √74

Attachment:

2017-12-12_2126.png [ 4.02 KiB | Viewed 530 times ]

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In the figure above, if the x-coordinate of point R is 5, and the leng  [#permalink]

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14 Dec 2017, 10:21
Bunuel wrote:

In the figure above, if the x-coordinate of point R is 5, and the length of OR is 7, then the y-coordinate of point R is

(A) 2√3
(B) 4
(C) 2√6
(D) 4√3
(E) √74

Attachment:
2017-12-12_2126.png

Draw a line straight down from R to the x-axis. That point's coordinates are (5,0)

There is a right triangle, one leg = 5

Because it is a right triangle (sides / legs are perpendicular), the length of the other leg = triangle's height

height = y-coordinate of R because the line emanates from R

Find height with Pythagorean theorem:
$$5^2 + x^2 = 7^2$$
$$x^2 = 24$$
$$\sqrt{x^2} = \sqrt{4*6}$$
$$x = 2\sqrt{6}$$

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In the figure above, if the x-coordinate of point R is 5, and the leng   [#permalink] 14 Dec 2017, 10:21
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