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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the xy plane, the rectangular ABCD is placed such that AB is paral

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SVP  V
Joined: 23 Feb 2015
Posts: 2011
In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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3
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Difficulty:   85% (hard)

Question Stats: 40% (02:17) correct 60% (02:48) wrong based on 35 sessions

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Attachment: coordinate geometry...PNG [ 7.18 KiB | Viewed 546 times ]

In the xy-plane, the rectangle ABCD is placed such that AB is parallel to the x-axis and CB is the parallel to the y-axis. A right triangle, ABE not shown, is drawn inside the rectangle, such that side AB is the hypotenuse of the triangle, and point E is on side CD of the rectangle. Which of the following could be the x-coordinate of point E?

A) 2
B) 2.5
C) 3
D) 4
E) 5.25
PS Forum Moderator P
Joined: 18 Jan 2020
Posts: 1544
Location: India
GPA: 4
Re: In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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Y cordinate of E will be 3
Let X cordinate be x
Length of AB = 5

Length of one leg of right angle triangle = √(x-1)^2+(3-1)^2

Length of other leg of right angle triangle = √(x-6)^2+(3-1)^2

AB^2 = (x-1)^2+(3-1)^2 + (x-6)^2+(3-1)^2
25 = (x-1)^2 + 4 + (x-6)^2 + 4
17 = (x-1)^2 + (x-6)^2
17 = x^2+1-2x+x^2+36-12x
17-37 = 2X^2-14x
-20 = 2X^2-14x
-10 = X^2-7x
0 = X^2-7x+10
0 = X^2-5x-2x+10
0 = X(X-5)-2(X-5)
0 = (X-5)(X-2)
X = 5&2
Since 5 is not among options.

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Intern  B
Joined: 07 Mar 2020
Posts: 36
Location: India
Concentration: Finance, Accounting
Re: In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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2
1
IMO -A
Slope of perpendicular line is
M1*M2=-1
Slope of AE =(3-1)/(x-1)
Slope of BE =(1-2)/(6-x)

-1= 2/(x-1) *-2/(6-x)
X^2-7x+10=0
(X-5)(x-2)=0
X=2 &5
Only 2 is available in the option so answer is A

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Director  G
Joined: 16 Feb 2015
Posts: 657
Location: United States
Re: In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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Explanation:

We can easily solve this question by Options.

Checking Option A: x cordinate = 2
We know, AB=5 , Elies on Line CD (i.e. Y coordinate is 3).
So E (2,3)
Given: A(1,1) , B(6,1). ABCD is rectangle. C(6,3) D(1,3)
AE = √(2^2 + 1^2) = √5
BE= √(4^2 + 2^2) = √20
As ABE is right angle triangle
So, AE^2 + BE^2 = AB^2
(√5)^2 +(√20)^2 = AB^2
AB=√25 = 5

IMO-A
Manager  S
Joined: 17 Jun 2020
Posts: 126
Location: India
Concentration: Marketing, Sustainability
GMAT 1: 480 Q34 V20
Re: In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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is something wrong with the question? how can CD be parallel to the Y axis ? it should be parallel to x axis or AC should be parallel to Y-axis. Or m I interpreting it incorrectly ?
VP  V
Joined: 27 May 2012
Posts: 1076
Re: In the xy plane, the rectangular ABCD is placed such that AB is paral  [#permalink]

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VERBAL1 wrote:
is something wrong with the question? how can CD be parallel to the Y axis ? it should be parallel to x axis or AC should be parallel to Y-axis. Or m I interpreting it incorrectly ?

Hi VERBAL1,

There was a minor typo in the question, It has now been corrected.
_________________
- Stne Re: In the xy plane, the rectangular ABCD is placed such that AB is paral   [#permalink] 12 Jul 2020, 22:08

# In the xy plane, the rectangular ABCD is placed such that AB is paral  