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# What is the area enclosed of the region enclosed by y = |x – 1| + 2, x

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Math Expert
Joined: 02 Sep 2009
Posts: 65062
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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05 May 2020, 03:03
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Difficulty:

45% (medium)

Question Stats:

70% (02:08) correct 30% (02:20) wrong based on 64 sessions

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What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10

Are You Up For the Challenge: 700 Level Questions

_________________
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1138
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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05 May 2020, 06:36
Bunuel san, Is the question x not equal to 1?
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Joined: 12 Dec 2015
Posts: 526
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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05 May 2020, 07:39
2
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5 --> correct: y = |x – 1| + 2, so (1) x=1, y=2 & if you increase or decrease x, y will always increase linearly with slop of 1, and intersect y-axis (2) @x=0, y=3, so enclosure enclosed by x = 1, x–axis and y–axis looks like trapezium with height=1, and two unequal side length = 2&3, so the area= (1/2)*(2+3)*1=5/2=2.5
B. 5
C. 7
D. 9
E. 10
Intern
Joined: 16 Dec 2017
Posts: 1
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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26 May 2020, 23:59
1
hiranmay wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5 --> correct: y = |x – 1| + 2, so (1) x=1, y=2 & if you increase or decrease x, y will always increase linearly with slop of 1, and intersect y-axis (2) @x=0, y=3, so enclosure enclosed by x = 1, x–axis and y–axis looks like trapezium with height=1, and two unequal side length = 2&3, so the area= (1/2)*(2+3)*1=5/2=2.5
B. 5
C. 7
D. 9
E. 10

Hi,

How do we deal with the absolute sign in the equation above. We should be having 2 equations to remove the absolute sign on? One >0 and the other one <0?
Intern
Joined: 02 Jun 2019
Posts: 7
Location: India
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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02 Jun 2020, 19:19
While i am trying to put values in the x and y , i am not getting a trapezium. Can someone explain the plotting bit.
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Joined: 19 Oct 2018
Posts: 1989
Location: India
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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03 Jun 2020, 01:07
1
1
Attachment:

Untitled.png [ 7.7 KiB | Viewed 391 times ]

Area $$= (2*1)+\frac{1}{2} *1*1 = 2.5$$

Bunuel wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10

Are You Up For the Challenge: 700 Level Questions
Intern
Joined: 02 Jun 2019
Posts: 7
Location: India
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x  [#permalink]

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03 Jun 2020, 01:38
nick1816 wrote:
Attachment:
Untitled.png

Area $$= (2*1)+\frac{1}{2} *1*1 = 2.5$$

Bunuel wrote:
What is the area enclosed of the region enclosed by y = |x – 1| + 2, x = 1, x–axis and y–axis?

A. 2.5
B. 5
C. 7
D. 9
E. 10

Are You Up For the Challenge: 700 Level Questions

Thanks a lot! I understood my mistake, I did not understand the problem correctly.
x=1 was another line (represented as red in the graph).
Re: What is the area enclosed of the region enclosed by y = |x – 1| + 2, x   [#permalink] 03 Jun 2020, 01:38