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# In the figure above, RS = ST, and the coordinates of S are (k, 3). Wha

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Math Expert
Joined: 02 Sep 2009
Posts: 50571
In the figure above, RS = ST, and the coordinates of S are (k, 3). Wha  [#permalink]

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11 Dec 2017, 22:09
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:01) correct 13% (00:43) wrong based on 37 sessions

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In the figure above, RS = ST, and the coordinates of S are (k, 3). What is the value of k?

(A) – 3
(B) –√3
(C) 0
(D) √3
(E) 3

Attachment:

2017-12-12_1002.png [ 5.55 KiB | Viewed 524 times ]

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Joined: 22 May 2016
Posts: 2090
Re: In the figure above, RS = ST, and the coordinates of S are (k, 3). Wha  [#permalink]

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12 Dec 2017, 08:40
Bunuel wrote:

In the figure above, RS = ST, and the coordinates of S are (k, 3). What is the value of k?

(A) – 3
(B) –√3
(C) 0
(D) √3
(E) 3

Attachment:
The attachment 2017-12-12_1002.png is no longer available

Attachment:

sqcoord.png [ 6.7 KiB | Viewed 366 times ]

This figure is a square:
-- right angles at opposite corners mean two parallel sides are perpendicular to two other parallel sides
-- RS = ST. Equal sides of a shape with two sets of parallel and two sets of perpendicular lines mean the corresponding parallel sides (OT and OR), are equal

The length of RS is 3, taken from the difference in y-coordinates of vertex R and S
The y-coordinate of R is 0. y-coordinate, given, of S, is 3. (3 - 0) = 3

RS = ST = 3, which means that S must have a k-coordinate that makes length of ST = 3

The difference between the x-coordinates of T, call its x-coordinate t, and S, must = 3
t = 0
t - k = 3
0 - k = 3
-k = 3
k = -3

Re: In the figure above, RS = ST, and the coordinates of S are (k, 3). Wha &nbs [#permalink] 12 Dec 2017, 08:40
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